The following linear programming model formulation is used for the production of four different products, with two different manufacturing processes and two different material requirements:

maximize Z = 50x1 + 58x2 + 46x3 + 62x4 subject to 4x1 + 3.5x2 + 4.6x3 + 3.9x4 … 600 hr. (process 1)

2.1x1 + 2.6x2 + 3.5x3 + 1.9x4 … 500 hr. (process 2)

15x1 + 23x2 + 18x3 + 25x4 … 3,600 lb. (material A)

8x1 + 12.6x2 + 9.7x3 + 10.5x4 … 1,700 lb. (material B)

x1 + x2 x1 + x2 + x3 + x4

Ú .60 x1, x2, x3, x4 Ú 0

a. Solve this problem by using the computer.

b. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.

c. Which is the most valuable resource to the firm?

d. One of the four products is not produced in the optimal solution. How much would the profit for this product have to be for it to be produced?