Operations Managment Appendix A

Question 4

Please explain and show work. Thank you.

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 MAEHINE TYPE x1 x2 x3 Milling machine 4 5 T Lathe 3 5 G Grinder 9 B 3 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines ?6@ Lathes 556 Grinders 166 The salespeople estimate they can sell all the units of X1 and X2 that can be made. But the sales potential of X3 is 110 units per week maximum. Unit profits for the three products are UNIT PROFITS X1 $ 46 X: 35 X3 31 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.) --- 5.1 Milling Grinders Sales X112: X32 U 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.} Resources Used Milling Lathes Grinders Sales :. How much of each constraint or resource is unused? {Leave no cells blank - be certain to enter \"0" wherever required. Round your answers to the nearest whole number.) Slack Variables 51 S2 53 34 d-1. I|Mould the machines work at capacity? Milling machines Grinders d-2. Will X3 be at maximum sales capacity? 0 No 0 Yes e. Suppose that an additional 27'5 hours per week can be obtained from the Milling machine by working overtime. The incremental cost would be $3.50 per hour. What would be the allowable increase (from the excel sensitivity report) in overtime when compared to additional hours that can be obtained? {Round \"shadow price\" to 2 decimal places and the rest to the nearest whole number.) The allowable increase (from the Excel sensitivityr report} in overtime is _ the additional hours that can he obtained