Question: You are given the following linear programming model in algebraic form, with x1 and x2 as the decision variables: Minimize Cost = 40x1 + 50x2

  1. You are given the following linear programming model in algebraic form, with x1 and x2 as the decision variables:

Minimize Cost = 40x1 + 50x2

Subject to:

Constraint 1: 2x1 + 3x2 30

Constraint 2: x1 + x2 12

Constraint 3: 2x1 + x2 20

And

x1 0 x2 0

1a. Use the graphical method to solve this model.

1b. Hoe does the optimal solution change if the objective function is changed to Cost= 40x1 + 70x2?

1c. How does the optimal solution change if the third functional constraint is changed to 2x1 + x2 15?

1d. What is Constraint 2 in the original problem called? And why?

1e. How does the optimal solution change if the objective function changed to MAXIMIZE cost = 40x1 +50x2?

1f. How does the optimal solution change if a new constraint (2x1 + 4x2 16) added to the original problem?

1g. How does the optimal solution change if the objective function is changed to MINIMIZE cost = 10x1 + 15x2?

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