Q1 (10 pts). One of the many linear programming applications is in doing cost-to-benefit analysis. The objective is to select a combination of benefits so as to minimize the cost (premium) while satisfying all the benefits goals.

The decision variables here are the levels of four activities (A1, A2, A3 and A4). The linear programming formulation looks like as below:

Minimize Total Cost = 2A1 + A2 - A3 + 3A4

Subject to:

Benefit 1: 3A1 + 2A2 - 2A3 +5A4 80

Benefit 2: A1 - A2 +A4 10

Benefit 3: A1 + A2 - A3 +2A4 30

A1, A2, A3, A4 are all greater than or equal to 0.

a. Solve this problem using Solver, and save results and sensitivity analysis. Write down and interpret the solution.

b. Which constraints are binding? If you relax the first constraint to 79, what will be the impact on the total cost? If you increase the second constraint to 11, what will be the impact on the total cost? (Note: Look at the sensitivity analysis to answer this question.)

c. If the cost of A1 was decreased to 1, what will be the impact on the solution? (Note: Look at the sensitivity analysis to answer this question.)