Suppose that Par, Inc., management encounters the following situations:

a.The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag.
b. A new low-cost material is available for the standard bag, and the profit contribution per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.)
c. New sewing equipment is available that would increase the sewing operation capacity to 750 hours. (Assume that 10A + 9B is the appropriate objective function.)

Required:
If each of these situations is encountered separately, what is the optimal solution and the total profit contribution?

We have the assumption that the function to be equals to 10A + 9B. The first step that we need to take here is to find the constraint for the linear programming relaxation which is;

1/2A + 5/6B [tex]\leq[/tex] 600.

1/10A + 1/4B [tex]\leq[/tex] 135. Thus, A [tex]\geq[/tex]0 and B

With the help of excel solver and graphs, that we have the profit at $18 we are going have the value of A =300 and B =420. Therefore, the optimal solution = [300,420].

Thus, we have the objective function value to be = 10,560. [that is 10 * 300 + 420 * 18}.

[b]. For option b, where the profit increases to $20, the optimal solution lies on A =708 and B =0. Hence, objective function value = 14,160[ that is 20 * 708 + 0].

[c]. Here, there is increase in the sewing operation capacity to 750 hours. Therefore, we will have the value of A = 540 and B = 252.

Thus, the objective function value = 7668.