Answer:
[a]. 10560, [b]. 14160, [c]. 7668.
Explanation:
[a]. In order to be able to solve this particular question we have to consider what is known as LINEAR PROGRAMMING.
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 600.
1/10A + 1/4B 135. Thus, A
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.