1. Let x = number of units of product 1 to produce and let y = number of units of product 2 to produce. Consider the following objective function: Maximize z = x + 2y. Subject to the following constraints: x + y ≤ 12 (resource A), x ≤ 8 (resource B), y ≤ 6 (resource C), x and y ≥ 0. What will the optimal objective function value be?
1. Let x = number of units of product 1 to produce and let y = number of units of product 2 to produce. Consider the following objective function: Maximize z = x + 2y. Subject to the following constraints: x + y ≤ 12 (resource A), x ≤ 8 (resource B), y ≤ 6 (resource C), x and y ≥ 0. What will the optimal objective function value be?
2. Refer to Question #1. Suppose the amount resource A available is increased from 12 to 14. Now what will the optimal objective function value be?
3. Refer to Question #1. Suppose the amount resource B available is increased from 8 to 10. Now what will the optimal objective function value be?
4. Refer to Question #1. What is the shadow price for the resource C constraint?
5. Consider a scenario with an objective function Minimize $14X + $17Y. Assume that the value of X in the optimal solution is zero and the reduced cost for variable X is $3. At what objective function coefficient will X first become part of the optimal solution?
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