A manufacturing firm has discontinued production of a certain unprofitable product line.Considerable excess production capacity was created as a result. Management is consideringdevoting this excess capacity to one or more of three products: X1, X2, and X3.Machine hours required per unit arePRODUCTMACHINE TYPE X1 X2 X3Milling machine 8 2 3Lathe 4 3 0Grinder 2 0 1The available time in machine hours per week isMACHINE HOURS PER WEEKMilling machines 800Lathes 480Grinders 320The salespeople estimate that they can sell all the units of X1 and X2 that can be made. But thesales potential of X3 is 80 units per week maximum.Unit profits for the three products areUNIT PROFITSX1 $20X2 6X3 8a. Set up the equations that can be solved to maximize the profit per week.b. Solve these equations using the Excel Solver.c. What is the optimal solution? How many of each product should be made, and what shouldthe resultant profit be?d. What is this situation with respect to the machine groups? Would they work at capacity, orwould there be unused available time? Will X3 be at maximum sales capacity?e. Suppose that an additional 200 hours per week can be obtained from the milling machinesby working overtime. The incremental cost would be $1.50 per hour. Would you recommenddoing this? Explain how you arrived at your answer.
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