Problem A-3 (Algo) A manufacturing firm has discontinued production of a certain unprofitable product line. Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X1, X2, and X3 Machine hours required per unit are PRODUCT MACHINE TYPE X1 X2 Ex Milling machine 4 Lathe Grinder 2 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines 890 Lathes 410 Grinders 278 The salespeople estimate they can sell all the units of X, and X2 that can be made. But the sales potential of X3 is 120 units per week maximum. Unit profits for the three products are UNIT PROFITS X1 $ 16 X2 12 X3 11 a. Set up the equations that can be solved to maximize the profit per week. (Leave no cells blank - be certain to enter "0" wherever required.) Maximize Z = X1 + X2 + X3S.t Milling X1 + X2 + X3 s Lathes X1 + X2 + X3 s Grinders X1 + X2 + X3 5 Sales X1 + X2 + X3 5 X1, X2, X3 2 b. Solve these equations using the Excel Solver. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to the nearest whole number.) Decision for X1 Decision for X2 Decision for X3 Total profitResources Used Milling Lathes Grinders Sales c. How much of each constraint or resource is unused? (Leave no cells blank - be certain to enter "O" wherever required. Round your answers to the nearest whole number.) Slack Variables Hours 51 52 53 54 d-1. Would the machines work at capacity? Milling machines Lathes Grinders