Hoja1zx1x2x3x4x5x6solz1-20-10-1000000x4031051005016 2/3x50401010102 1/2x60694001203 1/3renglon x5/4zx1x2x3x4x5x6solz1-20-10-100000x40310510050x50101/401/402 1/2pivotex6069400120(z)-((-20)(x5))zx1x2x3x4x5x6solz10-10-505050x400104 1/41-3/4042 1/2x10101/401/402 1/2x60092 1/20-1 1/215zx1x2x3x4x5x6solz10-10-505050-5x400104 1/41-3/4042 1/24 1/4x10101/401/402 1/20x60092 1/20-1 1/2155/9x6/9zx1x2x3x4x5x6solz10-10-505050x400104 1/41-3/4042 1/2x10101/401/402 1/2x20015/180-1/61/95/9pivote

zx1x2x3x4x5x6solz100-2 2/903 1/31 1/955 5/9x40001 17/36111/12-1 1/936 17/18x10101/401/402 1/2x20012/70-1/61/95/9zx1x2x3x4x5x6solz100-2 2/903 1/31 1/955 5/9-25x40001 17/36111/12-1 1/936 17/1825 5/53x10101/401/402 1/210x20015/180-1/61/95/92x2 / 5/18zx1x2x3x4x5x6solz100-2 2/903 1/31 1/955 5/9x40001 17/36111/12-1 1/936 17/18x10101/401/402 1/2x2 003 3/510-3/52/52pivote

zx1x2x3x4x5x6solz108002260x400-5 3/10011 4/5-1 7/1034x101-9/10002/5-1/102x3003 3/510-3/52/52EJERCICIO FINALIZADO3.9285714286

Hoja2150 x1 + 210 x2 + 130 x310 x1 + 15 x2 + 7 x3 330012 x1 + 17 x2 + 7 x3 3500modelo matematico8 x1 + 9 x2 + 8 x3 2900X1, x2, x3 0forma estandarMAX Z 150 x1 -210x2 -130x3 = 0 10 x1 + 15 x2 + 7 x3 + x4 = 3300 12 x1 + 17 x2 + 7 x3 + x5 = 3500 8 x1 + 9 x2 + 8 x3 + x6 = 2900zx1x2x3x4x5x6solz1-150-210-13000000x40101571003300220x50121770103500205 15/17pivotex608980012900322 2/9x5/17zx1x2x3x4x5x6solz1-150-210-1300000x40101571003300x2012/1717/1701/170205 15/17x608980012900operacioneszx1x2x3x4x5x6solz1-1 13/170-43 9/17012 6/17043235 5/17x40-10/17014/171-15/170211 13/17x2012/1717/1701/170205 15/17x601 11/1704 5/170-9/1711047 1/17repetimos procedimientoszx1x2x3x4x5x6solz1-1 13/170-43 9/17012 6/17043235 5/17-993 9/37x40-10/17014/171-15/170211 13/17257 1/7x2012/1717/1701/170205 15/17500x601 11/1704 5/170-9/1711047 1/17243 61/73pivotex6 / 4 5/17zx1x2x3x4x5x6solz1-1 13/170-43 9/17012 6/17043235 5/17x40-10/17014/171-15/170211 13/17x2012/1717/1701/170205 15/17x3028/73010-9/7317/73243 61/73operacioneszx1x2x3x4x5x6solz114 68/730006 72/7310 10/7353849 23/73x40-66/73001-57/73-14/7310 70/73x2040/731008/73-7/73105 35/73x3028/73010-9/7317/73243 61/73VALORESzx1x2x3x4x5x6solz114.93150684930006.986301369910.136986301453849.3150684931x40-0.904109589001-0.7808219178-0.191780821910.9589041096x200.54794520551000.1095890411-0.095890411105.4794520548x300.3835616438010-0.12328767120.2328767123243.8356164384EJERCICIO FINALIZADO

Hoja3MAX Z = X1 + 2 X2 + X3 SOLUCIN 2X1 + X2 + 3 X3 8 Z = 11.5 2X2 + 4X3 10 X1 = 1.5Modelo matematico X1 + X2 + X3 15 X2 = 5 X1 , X2 ,X3 0 X3 = 0Forma EstandarMAX Z -X1 - 2 X2 - X3 = 02 x1 + x2 + 3 x3+ x4 =8 2X2 + 4X3 +x5 =10X1 + X2 + X3 +x6 =15forma estandarzx1x2x3x4x5x6solz1-1-2-100000x4021310088x50024010105pivotex601110011515x5 / 2zx1x2x3x4x5x6solz1-1-2-10000x402131008x5001201/205x6011100115operacioneszx1x2x3x4x5x6solz1-10301010x402011-1/203x2011/21 1/21/2004x6010-10-1/2110repetimos procedimientoszx1x2x3x4x5x6solz1-10301010-10x402011-1/2031 1/2x2011/21 1/21/20044x6010-10-1/211010x4 / 2zx1x2x3x4x5x6solz1-10301010x10101/21/2-1/401 1/2pivotex2011/21 1/21/2004x6010-10-1/2110operacioneszx1x2x3x4x5x6solz1003 1/21/23/4011 1/2x10101/21/2-1/401 1/2x2001/2101/402 1/2x6000-1 1/2-1/2-1/418 1/2VALORESzx1x2x3x4x5x6solz1003.50.50.75011.5x10100.50.5-0.2501.5x2000.5100.2502.5x6000-1.5-0.5-0.2518.5EJERCICIO FINALIZADO

Hoja4MIN Z = 2X1 + 4 X2 + 6X3 SOLUCIN 2X1 + 4 X3 10 Z = X1 +2X2 + 2X3 20 X1 = 5modelo matematico X2 = 7.5 X1 , X2 ,X3 0 X3 = 0forma estandarMIN Z - 2X1 - 4 X2 - 6X3 = 0 SOLUCIN - 2X1 -4 X3 + 1x4 = -10 Z = -X1 -2X2 -2X3 +x5 = -20 X1 = 5 X2 = 7.5 X1 , X2 ,X3 0 X3 = 0tabla simplezx1x2x3x4x5solz1-2-4-6000x4020-410-10x50-1-2-201-20zx1x2x3x4x5solz1-2-4-60000x4020-410-102.5x50-1-2-201-2010zx1x2x3x4x5solz1-2-4-6000x40-0.501-0.2502.5x50-1-2-201-20variable entra1-2-2-301variable salezx1x2x3x4x5solz-1-1-401.500x40-0.501-0.2502.5x5-2-2-20-0.51-2010.5-10-2101nueva tabla (las formulas estan en la libreta)