19. Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manu- factured by Brooklyn are contemporary and farmhouse. Contemporary style cabinets sell for $90 and farmhouse style cabinets sell for $85. Each cabinet produced must go through carpentry, painting, and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet. Hours per Process Style Carpentry Painting Finishing Contemporary 2.0 1.5 1.3 Farmhouse 2.5 1.0 1.2 Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour; and the weekly number of hours available in the processes is 3000 in carpentry, 1500 in painting, and 1500 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 500 contemporary cabinets and 650 farmhouse style cabinets each week. Let x = the number of contemporary style cabinets produced each week y = the number of farmhouse style cabinets produced each week a. Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit. b. Show the mathematical expression for each of the constraints on the three processes. c. Show the mathematical expression for each of Brooklyn Cabinets’ contractual agreements.

19. Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manu- factured by Brooklyn are contemporary and farmhouse. Contemporary style cabinets sell for $90 and farmhouse style cabinets sell for $85. Each cabinet produced must go through carpentry, painting, and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet. Hours per Process Style Carpentry Painting Finishing Contemporary 2.0 1.5 1.3 Farmhouse 2.5 1.0 1.2 Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour; and the weekly number of hours available in the processes is 3000 in carpentry, 1500 in painting, and 1500 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 500 contemporary cabinets and 650 farmhouse style cabinets each week. Let x = the number of contemporary style cabinets produced each week y = the number of farmhouse style cabinets produced each week a. Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit. b. Show the mathematical expression for each of the constraints on the three processes. c. Show the mathematical expression for each of Brooklyn Cabinets’ contractual agreements.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 14P

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