handout02solutions

# handout02solutions - IEOR 162 Linear Programming Spring...

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IEOR 162 Linear Programming Spring 2007 Discussion Section Handout 2 Solutions 1. Basic solutions are (0,0), (1.5,0), (2,0), (3,0), (1,1), (0,1.5), (0,2), (0,3). Basic feasible solutions are (0,0), (1.5,0), (1,1), (0,1.5). Degenerate solution is (1,1) since 3 constraints are active at that point. 2. Basic solutions are (0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0), and all of these are feasible as well. The only degenerate solution is (0,0,1). 3. Variables: x ij = Amount of drug i produced from chemical j Formulation: max 2 x 12 - x 21 + x 22 s.t. . 7( x 11 + x 12 ) x 11 (1) . 6( x 21 + x 22 ) x 22 (2) x 11 + x 12 40 (3) x 21 + x 22 30 (4) x 11 + x 21 45 (5) x 12 + x 22 40 (6) x 11 , x 12 , x 21 , x 22 0 (7) First note that x 11 + x 12 represents the total amount of drug 1 produced and similarly x 21 + x 22 represents the total amount of drug 2 produced. Also note that the amount of chemical 1 used is x 11 + x 21 and the amount of chemical 2 used is x 12 + x 22 . So the objective is equal to maximizing proﬁt, which is revenue
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