Question

A company that manufactures three products, A. & and using three machines, M1, M2, and M3, wants to determine the optimal production schedule the maximizes the total profit. Product A has to be processed by machines M1, M2, and M3, product B requires M1 and M3, while product requires M1 and M2. The unit profits on the three products are $5,54 and 56, respectively. The following linear program is formulated to determine the optimal product mic Maximize S. Z-5x - 4x + 6x X1 - 2x + XS 430 (Machine 1) 3x - 2x S 460 (Machine 2) $ 450 (Machine 3) where x, X, and xs are the amounts of products AB and Cand the constraints reflect the available capacities of M1, M2, and M2. The optimum solution for the problem is as follows: following figures are hypothetical optimal solution : Xi =0, x= 120, x) = 260 optimal value: maximum profit 2 - 1450 shadow prices 2.0, 4.0, and 0.0 for constraints 1, 2 and 3 respectively reduced costs forx - 4.0, for x = 0, for x) = 0 RANGES ON RIGHT HAND SIDE (RHS) CONSTRAINTS Row Lower Limit Present Value Upper Limit 230 430 455 2 410 460 860 3 400 450 1 RANGES ON OBJECTIVE FUNCTION COEFFICIENTS Variable Lower Limit Present Value Upper Limi 5.0 7.0 0 10.0 3.0 6.0 Using the above information answer the following question Due to an improvement in product design, the unit profit on product A can be increased to $7. Is it worthwhile producing product A now? Select the correct answer

Answer 1

Option-1 is correct

The upper limit of profit per unit of A is $7 and it has been increased to $7 as well. So, since the upper limit is not crossed, the optimal solution of x1=0 will remain the same and the objective will also remain the same.