You are given a linear programming problem. Maximize P = 6x + 4y subject to 2x + 3y ≤ 12 Resource 1 2x + y ≤ 8 Resource 2 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1. (e) Identify the binding and nonbinding constraints. constraint 1 constraint 2

You are given a linear programming problem. Maximize P = 6x + 4y subject to 2x + 3y ≤ 12 Resource 1 2x + y ≤ 8 Resource 2 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1. (e) Identify the binding and nonbinding constraints. constraint 1 constraint 2

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter8: Evolutionary Solver: An Alternative Optimization Procedure

Section8.5: Combinatorial Models

Problem 7P

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