please slove D and E options. dont slove a b c

1. (30 pts.) A company that manufactures three products, A, B, and C, using three machines, MI, 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 B requires M1 and M3, while product C requires Ml and M2. The unit profits on the three products are $4, $2, and $5, respectively. The following linear program is formulated to determine the optimal product mix: Maximize Z = 4x1 + 2x2 + 5x3 S.t. 3x1 xi + 2x2 + x3 0 where x1, x2, and x3 are the amounts of products A, B, and C and the constraints reflect the available capacities of MI, M2, and M3. The optimum solution for the problem is as follows: optimal solution : x1=0, x2 = 100, x3 = 230 optimal value: maximum profit, Z= 1350 shadow prices: 1.0, 2.0, and 0.0 for constraints 1, 2 and 3 respectively reduced costs : for x1 = 3.0, 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 RANGES ON OBJECTIVE FUNCTION COEFFICIENTS Variable Lower Limit Present Value Upper Limit Xi 4.0 7.0 X2 0 2.0 10.0 X3 3.0 5.0 00 Using the above information answer the following questions: a. c. Because of an increase in the cost of raw material used for product C, its unit profit drops to $4. Determine the new optimal solution and the maximum profit. b. Suppose it is possible to increase the capacity of one of the machines. Which one would you recommend for expansion and why? Due to an improvement in product design, the unit profit on product A can be increased to $6. Is it worthwhile producing product A now? Explain. d. Suppose that the capacity of machine 2 can be increased by another 200 minutes at a cost of $250. Is it economical to do so? Explain. Because of an increase in the cost of energy for operating the machines, the unit profits of A, B, and C decrease by $2.0, $0.5, and $1.0, respectively. How will it affect the optimal solution and maximum profit? e