4. Consider the following problem Maximize Z = 3x₂ + 2x₂ subject to x₁ ≤4 2x₂ ≤ 12 3x₂ + 2x₂ ≤ 15 and x₁ ≥ 0, x₂ ≥ 0 (a) Construct the dual problem for this primal problem. (b) The simplex method is used to solve the primal problem step by step, the initial and resulting tableau after each iteration are given below. For each iteration, identify the BF solution for this problem and the complementary basic solution for the dual problem. Iteration 0 BV Eq Eq(0) Z s1 Eq(1) s2 Eq(2) s3 Eq(3) Iteration 1 BV Eq Z Eq(0) x1 Eq(1) s2 Eq(2) s3 Eq(3) Iteration 2 BV Eq Z Eq(0) x1 Eq(1) s2 Eq(2) x2 Eq(3) Z 1 0 0 0 N1OOO Z 0 0 NLOOO Z 1 0 0 0 x1 -3 3103 x1 0 1 0 x1 0 1 0 x2 -2 7022 x2 -2 0 2 2 x2 0 0 0 1 s1 ооно 43103 s1 -3 s1 ܐ ܘ ܝ ܚ ܩ -1.5 s2 0 0 s2 ZOOLO 0 0 1 0 s2 0 1 0 s3 0 0 1 s3 30001 s3 1 0 -1 0.5 RHS 4 12 15 RHS 12 4 12 3 RHS 15 54 4 9 1.5
4. Consider the following problem Maximize Z = 3x₂ + 2x₂ subject to x₁ ≤4 2x₂ ≤ 12 3x₂ + 2x₂ ≤ 15 and x₁ ≥ 0, x₂ ≥ 0 (a) Construct the dual problem for this primal problem. (b) The simplex method is used to solve the primal problem step by step, the initial and resulting tableau after each iteration are given below. For each iteration, identify the BF solution for this problem and the complementary basic solution for the dual problem. Iteration 0 BV Eq Eq(0) Z s1 Eq(1) s2 Eq(2) s3 Eq(3) Iteration 1 BV Eq Z Eq(0) x1 Eq(1) s2 Eq(2) s3 Eq(3) Iteration 2 BV Eq Z Eq(0) x1 Eq(1) s2 Eq(2) x2 Eq(3) Z 1 0 0 0 N1OOO Z 0 0 NLOOO Z 1 0 0 0 x1 -3 3103 x1 0 1 0 x1 0 1 0 x2 -2 7022 x2 -2 0 2 2 x2 0 0 0 1 s1 ооно 43103 s1 -3 s1 ܐ ܘ ܝ ܚ ܩ -1.5 s2 0 0 s2 ZOOLO 0 0 1 0 s2 0 1 0 s3 0 0 1 s3 30001 s3 1 0 -1 0.5 RHS 4 12 15 RHS 12 4 12 3 RHS 15 54 4 9 1.5
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...
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