The following is a linear programming model for analyzing the product mix of Maxine€™s hat Company, which produces three hat styles:
Maximize: $7x1+ $8x2 + $6x3 = Z
Subject to: 2x1 + 4x2 + 2x3 ‰¤ 120 (machine A time)
5x1 + 3x2 + 2x3 ‰¤ 400 (machine B time)
2x1+ 2x2 + 4x3 ‰¤ 110 (machine C time)
x1 ‰¥ 0x2 ‰¥ 0, and x3 ‰¥ 0
€˜The POM for Windows printout in Figure E.17 shows the optimal solution to the problem. Consider each of the following statements independently, and state whether it is true or false. Explain each answer.

a. If the price of hat 3 were increased to $11.50, it would be part of the optimal product mix.
b. The capacity of machine B can be reduced to 280 hours without affecting profits.
c. If machine C had a capacity of 115 hours, the production output would remainunchanged.

(a) Results Screen X1 RHS | Shadow Price Maximize Machine A Machine B Machine C Selution> 120 400 110 (b) Ranging Screen Variable ValueReducedst original Val Lower Bound Upper Bound 4.6667 Infinity 13 Shadow Price Slack Sutplus Original Val 120 400 110 Lower Bound 110 265 60 Upper Bound Constraint Machine A Machine B Machine C Infinity 120 135