HW2_soln

# HW2_soln - IEOR162 Spring 09 Solution for Homework 2 3.1.5...

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IEOR162 Spring 09 Solution for Homework 2 3.1.5 If there are > and or < constraints, then a problem may have no optimal solution. Consider the problem max z = x s.t. x<1. Clearly, this problem has no optimal solution (there is no largest number smaller than 1!!) 3.2.5 Let x 1 = desks produced, x 2 = chairs produced. LP formulation is max z = 40x 1 + 25x 2 s.t. -2x 1 + x 2 0 4x 1 + 3x 2 20 x 1 , x 2 0 Graphically we find the optimal solution to be x 1 = 2, x 2 = 4 and z = 180. 3.2.6 Let W = acres of wheat planted and C = acres of corn planted. Then the appropriate LP is max z = 200W + 300C s.t. W + C 45 (Land) 3W + 2C 100 (Workers) 2W + 4C 120 (Fertilizer) W, C 0 Graphically solving this LP we find the optimal solution to be z = \$10,000, W = C = 20 acres.

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IEOR162 Spring 09 Solution for Homework 2 3.3.4 AB is 2x 1 + x 2 = 6; CD is x 1 + 3x 2 = 9. The feasible region is bounded by AECF. Dotted line is 3 = 3x
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## HW2_soln - IEOR162 Spring 09 Solution for Homework 2 3.1.5...

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