A manufacturing fi rm has discontinued production of a certain unprofi table 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 they can sell all the units of X1 and X2 that can be made. Butthe sales potential of X3 is 80 units per week maximum.Unit profi ts for the three products areUnit ProfitsX1 $20X2 6X3 8a. Set up the equations that can be solved to maximize the profi t 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 whatshould the resultant profi t be?d. What is this situation with respect to the machine groups? Would they work at capacity,or would 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 using staff overtime. The incremental cost would be $1.50 per hour. Wouldyou recommend doing this? Explain how you arrived at your answer.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A manufacturing fi rm has discontinued production of a certain unprofi table 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 X3
Milling machine 8 2 3
Lathe 4 3 0
Grinder 2 0 1
The available time in machine hours per week is
Machine Hours per Week
Milling machines 800
Lathes 480
Grinders 320
The salespeople estimate they can sell all the units of X1 and X2 that can be made. But
the sales potential of X3 is 80 units per week maximum.
Unit profi ts for the three products are
Unit Profits
X1 $20
X2 6
X3 8
a. Set up the equations that can be solved to maximize the profi t 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
should the resultant profi t be?
d. What is this situation with respect to the machine groups? Would they work at capacity,
or would 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 machines
by using staff overtime. The incremental cost would be $1.50 per hour. Would
you recommend doing this? Explain how you arrived at your answer.

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