Maxine's Hat Company produces three distinct hat styles. The operations manager has modeled the operations using linear programming. He is using x1, x2, x3 to represent each hat style.

Below is his formulation:

Maximize Z = 70x1 + 80x2 + 60x3

Subject to:

Machine A: 2x1 + 4x2 + 2x3 ≤ 120 hours
Machine B: 5x1 + 3x2 + 2x3 ≤ 400 hours
Machine C: 2x1 + 2x2 + 4x3 ≤ 110 hours
x1 ≥ 0; x2 ≥ 0; x3 ≥ 0

a. Use Excel to find the optimal solution for this problem. Provide printouts of worksheets for the final solution and the sensitivity report. Then consider the statements below independently, state whether they are true or false and explain each answer.

b. If the price of Hat 3 were to be increased by $55, it would be part of the optimal product mix.

c. The capacity of Machine B can be reduce to 280 hours without affecting profits.

d. If machine C had a capacity of 115 hours, the production output would remain unchanged.

Additional Requirement

These questions are belongs to the Operations Management and they defines about the process of producing 3 styles of hats by machines A, B and C. By using Excel and optimal solution has to be found.