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{\title Universidad de Costa Rica                                          Matematicas para Economia MA-232}{\author Hugo Alexander Chavarria}{\operator Hugo Alexander Chavarria}{\creatim\yr1998\mo8\dy8\hr11\min50}{\revtim\yr1998\mo8\dy8\hr18\min45}
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\par Facultad de Ciencias                                                    1 de Junio de 1996
\par Escuela de Matem\'e1tica 
\par 
\par }\pard\plain \s1\qc\keepn\nowidctlpar\widctlpar\outlinelevel0\adjustright \b\fs22\ul\lang1034\cgrid {II Examen Parcial
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00003d000a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01000004000000f0010100030000000000}}}}}{\fs22\lang1034  sujeta a la restricci\'f3n  }{\pard\plain \fi-360\li360\nowidctlpar\widctlpar
\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec }\ls1\adjustright \fs22\lang1034\cgrid {\object\objemb\objw1400\objh660{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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2ab826c3bd0103000000800100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000720000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff05000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000462300
00004d6963726f736f667420456469746f72206465206563756163696f6e657320332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020094d44c00000000000000185b4900806d49000000000003010103000a01030e00000102883100000112837800000002862b00030e00000102883100000112837900000002862b00030e0000010288310000011283
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000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000068000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400a509000074fbffff740200000800a5098c040000
010009000003350100000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022004c0081200000026060f001a00ffffffff000010000000c0ffffffb5ffffff80080000d50300000b0000002606
0f000c004d617468547970650000e00009000000fa02000001000000000000002200040000002d01000005000000140200024000050000001302000236010500000014020002c7020500000013020002d503050000001402000266050500000013020002440615000000fb0280fe00000000000090010000000004020010
54696d6573204e657720526f6d616e006c00040000002d01010008000000320a6002cd0701000000310008000000320a7001750501000000310008000000320a7001ee0201000000310008000000320a70015b0001000000310010000000fb0280fe0000000000009001000000020002001053796d626f6c000004000000
2d01020004000000f001010008000000320a6002b706010000003d0008000000320a60023404010000002b0008000000320a60029501010000002b0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e006c00040000002d01010004000000f001020008000000320a8a03
8f05010000007a0008000000320a8a03080301000000790008000000320a8a036e000100000078000a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01020004000000f0010100030000000000ffff}{\result {
\dn28\lang1034 {\pict{\*\picprop\shplid1027{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}
{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}}
\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0\picw2469\pich1164\picwgoal1400\pichgoal660\wmetafile8\bliptag1732082200\blipupi-979{\*\blipuid 673d7a18bc3edb1569740874589698e5}
010009000003350100000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022004c0081200000026060f001a00ffffffff000010000000c0ffffffb5ffffff80080000d50300000b00000026060f00
0c004d617468547970650000e00009000000fa02000001000000000000002200040000002d010000050000001402000240000500000013020002360105000000
14020002c7020500000013020002d503050000001402000266050500000013020002440615000000fb0280fe0000000000009001000000000402001054696d65
73204e657720526f6d616e006c00040000002d01010008000000320a6002cd0701000000310008000000320a7001750501000000310008000000320a7001ee02
01000000310008000000320a70015b0001000000310010000000fb0280fe0000000000009001000000020002001053796d626f6c0000040000002d0102000400
0000f001010008000000320a6002b706010000003d0008000000320a60023404010000002b0008000000320a60029501010000002b0015000000fb0280fe0000
000000009001010000000402001054696d6573204e657720526f6d616e006c00040000002d01010004000000f001020008000000320a8a038f05010000007a00
08000000320a8a03080301000000790008000000320a8a036e000100000078000a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01020004000000f001010003000000000000000000000000ffffff}}}}}{\fs22\lang1034 
.   Para clasificar los puntos cr\'edticos, utilice el criterio de la matriz(}{\f3\fs22\lang1034 \'64}{\fs22\lang1034\super 2}{\fs22\lang1034 L)(Criterio de la matriz Hessiana Orlada).
\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 3.\tab}}\pard \qj\fi-360\li360\nowidctlpar\widctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxta .}}\ls1\adjustright {\fs22\lang1034 
De todos los puntos que pertenecen a las superficies de ecuaciones }{\pard\plain \qj\fi-360\li360\nowidctlpar\widctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec }\ls1\adjustright \fs22\lang1034\cgrid {\object\objemb\objw2079\objh360
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c00000000000004600000000000000000000000080f0
4bb826c3bd0103000000c00100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000720000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff0500000006000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000462300
00004d6963726f736f667420456469746f72206465206563756163696f6e657320332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020094d4680000000000000064684900506349000000000003010103000a0112835300030f01000b0102861e220011000a02823a0012837800030f00000b11010288320000000a02862b0012837900030f00000b1101
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000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000084000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400530e000085fdffffcc0100000800530e7b020000
010009000003e20000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02000200051200000026060f001a00ffffffff000010000000c0ffffffc5ffffffc0040000c50100000b0000002606
0f000c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e001900040000002d01000008000000320a6001120401000000300008000000320a60010101010000002c0010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0000040000002d01010004000000f001000008000000320a6001df02010000003d0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e001900040000002d01000004000000f001010008000000320a6001bf0101000000790008000000320a60014e00010000007800
0a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f0010000030000000000}{\result {\dn10\lang1034 {\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw3667\pich635\picwgoal2079\pichgoal360\wmetafile8\bliptag-1306050058\blipupi1058{\*\blipuid b22741f6edd37373d8c647514811651d}
010009000003e20000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c02000200051200000026060f001a00ffffffff000010000000c0ffffffc5ffffffc0040000c50100000b00000026060f00
0c004d617468547970650000500015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e001900040000002d010000
08000000320a6001120401000000300008000000320a60010101010000002c0010000000fb0280fe0000000000009001000000020002001053796d626f6c0000
040000002d01010004000000f001000008000000320a6001df02010000003d0015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e001900040000002d01000004000000f001010008000000320a6001bf0101000000790008000000320a60014e000100000078000a0000002606
0f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f0010000030000000000}}}}}{\fs22\lang1034  y  }{\pard\plain \qj\fi-360\li360\nowidctlpar\widctlpar
\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec }\ls1\adjustright \fs22\lang1034\cgrid {\object\objemb\objw2520\objh380{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000a091
53b826c3bd0103000000c00100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000720000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff0500000006000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000462300
00004d6963726f736f667420456469746f72206465206563756163696f6e657320332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020094d47c00000000000000546f49009c6d49000000000003010103000a0112835300030f01000b01028608220011000a02823a00030100000112837800028612220288330000029628000296290000030f00000b11
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000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000098000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c4550494354005d11000062fdffff5803000008005d119e020000
010009000003a70100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c026002c00f1200000026060f001a00ffffffff000010000000c0ffffffb1ffffff800f0000110200000b0000002606
0f000c004d617468547970650000500010000000fb020afee100000000009001000000020002001053796d626f6c0000040000002d01000008000000320abd01b40201000000280010000000fb020afee100000000009001000000020002001053796d626f6c0000040000002d01010004000000f001000008000000320a
bd01220601000000290015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e00ec97040000002d01000004000000f001010008000000320ac001c50e01000000340008000000320ac001660501000000330008000000320ac001fa01010000003a0015000000fb0220ff0000
000000009001000000000402001054696d6573204e657720526f6d616e000600040000002d01010004000000f001000008000000320a14018b0c01000000320008000000320a1401aa0901000000320008000000320af900990601000000320010000000fb0280fe0000000000009001000000020002001053796d626f6c
0000040000002d01000004000000f001010008000000320ac0018d0d010000003d0008000000320ac001980a010000002b0008000000320ac0018707010000002b0008000000320ac0014704010000002d0010000000fb0220ff0000000000009001000000020002001053796d626f6c0000040000002d01010004000000
f001000008000000320a2002fb0001000000ce0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e00ec97040000002d01000004000000f001010008000000320ac001d30b010000007a0008000000320ac001da0801000000790008000000320ac0014003010000007800
08000000320ac00140000100000053000a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f0010000030000000000ffff}{\result {\dn10\lang1034 
{\pict{\*\picprop\shplid1029{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw4445\pich670\picwgoal2520\pichgoal380\wmetafile8\bliptag-305046924\blipupi-28{\*\blipuid edd15a740f2ee0900bebfdf52f98db9c}010009000003a70100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c026002c00f1200000026060f001a00ffffffff000010000000c0ffffffb1ffffff800f0000110200000b00000026060f00
0c004d617468547970650000500010000000fb020afee100000000009001000000020002001053796d626f6c0000040000002d01000008000000320abd01b402
01000000280010000000fb020afee100000000009001000000020002001053796d626f6c0000040000002d01010004000000f001000008000000320abd012206
01000000290015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e00ec97040000002d01000004000000f0010100
08000000320ac001c50e01000000340008000000320ac001660501000000330008000000320ac001fa01010000003a0015000000fb0220ff0000000000009001
000000000402001054696d6573204e657720526f6d616e000600040000002d01010004000000f001000008000000320a14018b0c01000000320008000000320a
1401aa0901000000320008000000320af900990601000000320010000000fb0280fe0000000000009001000000020002001053796d626f6c0000040000002d01
000004000000f001010008000000320ac0018d0d010000003d0008000000320ac001980a010000002b0008000000320ac0018707010000002b0008000000320a
c0014704010000002d0010000000fb0220ff0000000000009001000000020002001053796d626f6c0000040000002d01010004000000f001000008000000320a
2002fb0001000000ce0015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e00ec97040000002d01000004000000
f001010008000000320ac001d30b010000007a0008000000320ac001da0801000000790008000000320ac001400301000000780008000000320ac00140000100
000053000a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f001000003000000000000000000000000ffffff}}}}}{\fs22\lang1034 , determine los mas cercanos la origen.  (Asuma qu
e los puntos cr\'edticos son precisamente los m\'ednimos buscados, No debe demostrar por ning\'fan criterio que son m\'ednimos, usted solo debe encontrar los puntos.)
\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 4.\tab}}\pard \fi-360\li360\nowidctlpar\widctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxta .}}\ls1\adjustright {\fs22\lang1034 
(a) Determine la matriz }{\pard\plain \fi-360\li360\nowidctlpar\widctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec }\ls1\adjustright \fs22\lang1034\cgrid {\object\objemb\objw300\objh320{\*\objclass Equation.3}{\*\objdata 0105000002000000
0b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000805a
64b826c3bd0103000000400100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000720000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par        (b) Determine la forma diferencial asociada a la matriz A.
\par 
\par        (c) \'bfEs A definida positiva, negativa o indefinida?
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7720526f6d616e005500040000002d01000004000000f001010008000000320ae001210401000000790008000000320ae0010c0101000000780015000000fb02
80fe0000000000009001010000000402001054696d6573204e657720526f6d616e002100040000002d01010004000000f001000008000000320a80014f030100
0000500008000000320a800145000100000050000a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01000004000000f001010003000000000000000000000000ffffff}}}}}{\fs22\lang1034 .   Si una econom\'ed
a domestica posee una ingreso de 8 para estos art\'edculos, determine:
\par }\pard \nowidctlpar\widctlpar\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 (a)\tab}}\pard \fi-360\li780\nowidctlpar\widctlpar\jclisttab\tx780{\*\pn \pnlvlbody\ilvl0\ls4\pnrnot0\pnlcltr\pnstart1\pnindent780\pnhang{\pntxtb (}{\pntxta )}}\ls4\adjustright {
\fs22\lang1034 La funci\'f3n lagrangiana y los niveles \'f3ptimos }{\pard\plain \fi-360\li780\nowidctlpar\widctlpar\jclisttab\tx780{\*\pn \pnlvlbody\ilvl0\ls4\pnrnot0\pndec }\ls4\adjustright \fs22\lang1034\cgrid {\object\objemb\objw440\objh340
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0200000002ce020000000000c000000000000046000000000000000000000000e046
b8b826c3bd0103000000400100000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000
0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000720000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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0000000000000000000000000000000000000000000000000000000000000000000000001c000000020094d4240000000000000064684900506349000000000003010103000a01031100000112837800000002822c0003110000011283790000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
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00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c45504943540008030000a8fdffffc00100000800080358020000
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0f000c004d617468547970650000500009000000fa02000001000000000000002200040000002d010000050000001402470040000500000013024700f60005000000140247009e0105000000130247006c0215000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e006c000400
00002d01010008000000320a8001bf0101000000790008000000320a80014e0001000000780015000000fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e004497040000002d01020004000000f001010008000000320a80010101010000002c000a00000026060f000a00ffffffff
01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f00102000300000000008f82}{\result {\dn10\lang1034 {\pict{\*\picprop\shplid1034{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw776\pich600\picwgoal440\pichgoal340\wmetafile8\bliptag941088499\blipupi2303{\*\blipuid 3817def32367d30eaa13483e8f5ea962}010009000003db0000000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c022002c0021200000026060f001a00ffffffff000010000000c0ffffffb9ffffff80020000d90100000b00000026060f00
0c004d617468547970650000500009000000fa02000001000000000000002200040000002d010000050000001402470040000500000013024700f60005000000
140247009e0105000000130247006c0215000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d616e006c00040000002d01
010008000000320a8001bf0101000000790008000000320a80014e0001000000780015000000fb0280fe0000000000009001000000000402001054696d657320
4e657720526f6d616e004497040000002d01020004000000f001010008000000320a80010101010000002c000a00000026060f000a00ffffffff010000000000
10000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f001020003000000000000000000000000ffffff}}}}}{\fs22\lang1034  de compra.
\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 (b)\tab}}\pard \fi-360\li780\nowidctlpar\widctlpar\jclisttab\tx780{\*\pn \pnlvlbody\ilvl0\ls4\pnrnot0\pnlcltr\pnstart1\pnindent780\pnhang{\pntxtb (}{\pntxta )}}\ls4\adjustright {
\fs22\lang1034 Determine el efecto de renta del consumidor o efecto en el cambio de presupuesto.
\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 (c)\tab}}\pard \fi-360\li780\nowidctlpar\widctlpar\jclisttab\tx780{\*\pn \pnlvlbody\ilvl0\ls4\pnrnot0\pnlcltr\pnstart1\pnindent780\pnhang{\pntxtb (}{\pntxta )}}\ls4\adjustright {
\fs22\lang1034 Que sucede con el precio del articulo x si la renta se cambia en dos unidades.
\par }\pard \nowidctlpar\widctlpar\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 6.\tab}}\pard \fi-360\li360\nowidctlpar\widctlpar\jclisttab\tx360{\*\pn \pnlvlbody\ilvl0\ls1\pnrnot0\pndec\pnstart1\pnindent360\pnhang{\pntxta .}}\ls1\adjustright {\fs22\lang1034 Dibuje:

\par }\pard \li567\nowidctlpar\widctlpar\tx567\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 (a)\tab}}\pard \fi-360\li840\nowidctlpar\widctlpar\jclisttab\tx840{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent840\pnhang{\pntxtb (}{\pntxta )}}\ls5\adjustright {
\fs22\lang1034 El conjunto de oportunidades correspondiente a las siguientes restricciones:
\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par }\pard \qc\nowidctlpar\widctlpar\tx567{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\pard\plain \qc\nowidctlpar\widctlpar\tx567{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright \fs22\lang1034\cgrid {\object\objemb\objw1500\objh1160
{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
0000000000000000000001000000720000000000000003004f0062006a0049006e0066006f0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012000201ffffffff04000000ffffffff000000000000000000000000000000000000000000000000
000000000000000000000000030000000400000000000000feffffff02000000fefffffffeffffff0500000006000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100feff030a0000ffffffff02ce020000000000c0000000000000462300
00004d6963726f736f667420456469746f72206465206563756163696f6e657320332e30000c0000004453204571756174696f6e000b0000004571756174696f6e2e3300f439b271000000000000000000000000000000000000000000000000000000000300000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000001c000000020094d4780000000000000064684900506349000000000003010103000a010302010004010101028833001283780002862b00028834001283790002866422028836000001028612221283780002862b000288340012
837900030f00000b11010288320000000a028664220288320000011283780002822c00128379000286652202883000000002967b0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000004500710075006100740069006f006e0020004e00610074006900760065000000000000000000000000000000000000000000000000000000000000000000000020000200ffffffffffffffffffffffff000000000000
0000000000000000000000000000000000000000000000000000000000000400000094000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff00000000
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff0000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffff
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001050000050000000d0000004d45544146494c455049435400560a000002f8ffff480300000800560afe070000
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0a00000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01000004000000f0010100030000000000ffff}{\result {\dn52\lang1034 
{\pict{\*\picprop\shplid1035{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}{\sp{\sn fFlipV}{\sv 0}}{\sp{\sn pictureGray}{\sv 0}}{\sp{\sn pictureBiLevel}{\sv 0}}{\sp{\sn fillColor}{\sv 268435473}}{\sp{\sn fFilled}{\sv 0}}{\sp{\sn fHitTestFill}{\sv 1}}
{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw2646\pich2046\picwgoal1500\pichgoal1160\wmetafile8\bliptag452649974\blipupi-238{\*\blipuid 1afae3f681a058364c15fdb115371754}
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0c004d617468547970650000a00110000000fb0280fe0000000000009001000000020002001053796d626f6c0000040000002d01000008000000320aba054000
01000000ef0008000000320ad506400001000000ee0008000000320a2203400001000000ef0008000000320a4604400001000000ed0008000000320aad014000
01000000ec0008000000320a4006a40301000000b30008000000320a00042d0701000000a30008000000320a00044703010000002b0008000000320a00040501
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000004000000f001010008000000320a54032f0601000000320015000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
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ffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01000004000000f001010003000000000000000000000000ffffff}}}}}{\fs22\lang1034 
\par }\pard \nowidctlpar\widctlpar{\*\pn \pnlvlcont\ilvl0\ls0\pnrnot0\pndec }\adjustright {\fs22\lang1034 
\par {\pntext\pard\plain\fs22\lang1034\cgrid \hich\af0\dbch\af0\loch\f0 (b)\tab}}\pard \fi-360\li840\nowidctlpar\widctlpar\jclisttab\tx840{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pnlcltr\pnstart1\pnindent840\pnhang{\pntxtb (}{\pntxta )}}\ls5\adjustright {
\fs22\lang1034 Si una econom\'eda domestica prefiere adquirir a lo mas una unidad del articulo x(o sea, o 1 o menos de 1 unidad), dibuje de los gustos de esa econom\'eda, es decir: }{\pard\plain \fi-360\li840\nowidctlpar\widctlpar
\jclisttab\tx840{\*\pn \pnlvlbody\ilvl0\ls5\pnrnot0\pndec }\ls5\adjustright \fs22\lang1034\cgrid {\object\objemb\objw639\objh380{\*\objclass Equation.3}{\*\objdata 01050000020000000b0000004571756174696f6e2e33000000000000000000000c0000
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffdffffff04000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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0000000000000000000000001400000000000000010043006f006d0070004f0062006a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000120002010100000003000000ffffffff0000000000000000000000000000000000000000000000000000
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ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
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000026060f000a00ffffffff01000000000010000000fb021400090000000000bc02000000000102022253797374656d006e040000002d01010004000000f00100000300000000000100}{\result {\dn14\lang1034 {\pict{\*\picprop\shplid1036{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
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{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0
\picw1127\pich670\picwgoal639\pichgoal380\wmetafile8\bliptag1237694147\blipupi2306{\*\blipuid 49c5b6c3ee88b2b2ada02993bbef1e90}0100090000035f0100000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000
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Defina en que consiste el problema de la programaci\'f3n cl\'e1sica.
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Escriba de manera desarrollada las condiciones de Kuhn Tucker para el problema de programaci\'f3n no lineal dado por:
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