A company that manufactures three products, A, B, and using three machines, M1, M2, and M3, wants to determine the optimal production schedule that maximizes the total profit. Product A has to be processed by machines M1, M2, and M3, product requires M1 and M3, while product Crequires M1 and M2. The unit profits on the three products are 56, 56, and 57, respectively. The following linear program is formulated to determine the optimal product mix: Maximize s.t. Z = 6X1 + 6x2 + 7x3 X+ + 2x2 + x3 s 430 (Machine 1) 3x4 + 2x3 s 460 (Machine 2) X + 4x2 $ 450 (Machine 3) X1, X2, X3 20 where X1, X2, and X3 are the amounts of products A B, and C and the constraints reflect the available capacities of M1, M2, and M3. The optimum solution for the problem is as follows: following figures are hypothetical) optimal solution: X1 = 0, X2 = 130, X3 - 280 optimal value: maximum profit, Z = 1650 shadow prices: 4.0, 6.0, and 0.0 for constraints 1, 2 and 3 respectively reduced costs: for xy = 6.0, for X2 = 0, for x3 = 0 RANGES ON RIGHT-HAND-SIDE (RHS) CONSTRAINTS Row Lower Limit Present Value Upper Limit 1 230 430 455 2 410 460 860 3 400 450 00 RANGES ON OBJECTIVE FUNCTION COEFFICIENTS Variable Lower Limit Present Value Upper Limit X1 6.0 7.0 X2 0 6.0 10.0 X3 3.0 7.0 Using the above information answer the following question: Suppose it is possible to increase the capacity of one of the machines. Which one would you recommend for expansion and why? Your answer: m O Increase the capacity of machine 1, because it has a shadow price-4. Increase the capacity of machine 2, because it has the highest shadow price. o Increase the capacity of machine 3, because it has the lowest shadow price. Clear answer Pause test