lecture4

# lecture4 - Linear Programs Cars and Trucks symmetric form...

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e62: lecture 4 27/09/10 linear program symmetric form standard form Linear Programs 1 max cx s . t . Ax = b x 0 max cx s . t . Ax = b x 0 max cx s . t . Ax b x 0 max cx s . t . Ax b x 0 max cx s . t . A - A x b - b x 0 max cx s . t . Ax b max cx s . t . ± AI ² ³ x w ´ = b ³ x w ´ 0 max ± c - c ² ³ x + x - ´ s . t . ± A - A ² ³ x + x - ´ b ³ x + x - ´ 0 min cx s . t . Ax = b x 0 max ( - c ) x s . t . Ax = b x 0 e62: lecture 4 27/09/10 Cars and Trucks 2 1000 cars 1000 trucks proFt \$3M \$2.5M metal stamping capacity 4% 2.86% engine assembly capacity 3% 6% car assembly capacity 4.44% 0% truck assembly capacity 0% 6.67% strategy binding constraint units produced proft build cars car assembly 22500 \$67.5M build trucks truck assembly 15000 \$37.5M e62: lecture 4 27/09/10 LP Formulation 3 thousands of cars thousands of trucks max 3 x 1 +2 . 5 x 2 s . t . 4 . 44 x 1 100 auto assembly 6 . 67 x 2 100 truck assembly 4 x 1 . 86 x 2 100 metal stamping 3 x 1 +6 x 2 100 engine assembly x 1 0 x 2 0 Solution ! \$77.3M e62: lecture 4 27/09/10 Illustration 4 car assembly truck assembly metal stamping engine assembly c x 1 (thousands of cars) x 2

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e62: lecture 4 27/09/10 Feeding an Army 5 ingredient
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## This note was uploaded on 07/29/2011 for the course MS&E 111 at Stanford.

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lecture4 - Linear Programs Cars and Trucks symmetric form...

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