A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 960, 1020, and 840, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. Product A Product B Product C Dept. I Dept. II Dept. II Profit 2 1 2 3 1 2 2 $18 2 1 $12 $15 If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit? product A 0 product B 600 × product C 120 × What is the maximum profit (in dollars)? $ 1560 x

A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 960, 1020, and 840, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. Product A Product B Product C Dept. I Dept. II Dept. II Profit 2 1 2 3 1 2 2 $18 2 1 $12 $15 If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit? product A 0 product B 600 × product C 120 × What is the maximum profit (in dollars)? $ 1560 x

Essentials of Business Analytics (MindTap Course List)

2nd Edition

ISBN:9781305627734

Author:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Publisher:Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson

Chapter12: Integer Linear Optimization_models

Section: Chapter Questions

Problem 6P: Hart Manufacturing makes three products. Each product requires manufacturing operations in three...

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Rocks Industries has two products. They manufactured 12,539 units of product A and 8.254 units of product B. The data are: Â What is the activity rate for each cost pool?
Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows: During the next production period the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are 25 for product 1, 28 for product 2, and 30 for product 3. a. Formulate a linear programming model for maximizing total profit contribution. b. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution? c. After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are 400 for product 1, 550 for product 2, and 600 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs? d. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs provided in part (c) into account. Management also stated that we should not consider making more than 175 units of product 1, 150 units of product 2, or 140 units of product 3. e. Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c).
Rex Industries has two products. They manufactured 12,539 units of product A and 8.254 units of product B. The data are: What is the activity rate for each cost pool?
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