Cordova manufactures three types of stained glass windows, cleverly named Products A, B, and C. Information about these products follows: Sales price Variable costs per unit Fixed costs per unit Required number of labor hours Product A $ 47.00 22.70 9.00 1.50 14,000 units 9,000 units 10,000 units Product B $ 57.00 12.00 9.00 2.50 Product C $ 87.00 38.70 9.00 3.00 Cordova currently is limited to 58,500 labor hours per month. Cordova's marketing department has determined the following demar for its products: Product A Product B Product C Required: Given the company's limited resource and expected demand, compute how many units of each product Cordova should produce to maximize its profit. Note: Enter the products in the sequence of their preferences; the product with first preference should be entered first. Round your answers to the nearest whole number. Product Units Produced

Cordova manufactures three types of stained glass windows, cleverly named Products A, B, and C. Information about these products follows: Sales price Variable costs per unit Fixed costs per unit Required number of labor hours Product A $ 47.00 22.70 9.00 1.50 14,000 units 9,000 units 10,000 units Product B $ 57.00 12.00 9.00 2.50 Product C $ 87.00 38.70 9.00 3.00 Cordova currently is limited to 58,500 labor hours per month. Cordova's marketing department has determined the following demar for its products: Product A Product B Product C Required: Given the company's limited resource and expected demand, compute how many units of each product Cordova should produce to maximize its profit. Note: Enter the products in the sequence of their preferences; the product with first preference should be entered first. Round your answers to the nearest whole number. Product Units Produced

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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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).
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