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Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brookdyn are contemporary and farmhouse. Contemporary-style cabinets sell for $100 and farmhouse-style cabinets sell for $110. 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 2.3 1.6 1.4 Farmhouse 2.7 1.1 1.3 Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour; and the weekdy number of hours available in the processes is 2.400 in carpentry, 1.200 in painting, and 1.200 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 550 contemporary cabinets and 675 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. Max (b) Show the mathematical expression for each of the constraints on the three processes. carpentry painting finishing (c) Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements. contemporary farmhouse

Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brookdyn are contemporary and farmhouse. Contemporary-style cabinets sell for $100 and farmhouse-style cabinets sell for $110. 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 2.3 1.6 1.4 Farmhouse 2.7 1.1 1.3 Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour; and the weekdy number of hours available in the processes is 2.400 in carpentry, 1.200 in painting, and 1.200 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 550 contemporary cabinets and 675 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. Max (b) Show the mathematical expression for each of the constraints on the three processes. carpentry painting finishing (c) Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements. contemporary farmhouse

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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### Brooklyn Cabinets Production Planning **Introduction:** Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $100 and farmhouse-style cabinets sell for $110. Each cabinet produced must go through carpentry, painting, and finishing processes. The table below summarizes how much time in each process must be devoted to each style of cabinet: **Hours per Process:** | Style | Carpentry | Painting | Finishing | |---------------|-----------|----------|-----------| | Contemporary | 2.3 | 1.6 | 1.4 | | Farmhouse | 2.7 | 1.1 | 1.3 | **Costs and Constraints:** - Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour. - Weekly available hours: 2,400 in carpentry, 1,200 in painting, and 1,200 in finishing. - Contractual agreement: 550 contemporary cabinets and 675 farmhouse-style cabinets each week. **Let:** - \( x \) = number of contemporary-style cabinets produced each week - \( y \) = number of farmhouse-style cabinets produced each week ### Tasks: **(a) Objective Function:** Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit. Max \( \square \) **(b) Constraints:** Show the mathematical expression for each of the constraints on the three processes. - Carpentry: \( \square \) - Painting: \( \square \) - Finishing: \( \square \) **(c) Contractual Agreements:** Show the mathematical expression for each of Brooklyn Cabinets’ contractual agreements. - Contemporary: \( \square \) - Farmhouse: \( \square \) By formulating these constraints and the objective function, Brooklyn Cabinets can optimize their weekly production to maximize profit while adhering to operational constraints and contractual agreements.
Transcribed Image Text:### Brooklyn Cabinets Production Planning **Introduction:** Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $100 and farmhouse-style cabinets sell for $110. Each cabinet produced must go through carpentry, painting, and finishing processes. The table below summarizes how much time in each process must be devoted to each style of cabinet: **Hours per Process:** | Style | Carpentry | Painting | Finishing | |---------------|-----------|----------|-----------| | Contemporary | 2.3 | 1.6 | 1.4 | | Farmhouse | 2.7 | 1.1 | 1.3 | **Costs and Constraints:** - Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour. - Weekly available hours: 2,400 in carpentry, 1,200 in painting, and 1,200 in finishing. - Contractual agreement: 550 contemporary cabinets and 675 farmhouse-style cabinets each week. **Let:** - \( x \) = number of contemporary-style cabinets produced each week - \( y \) = number of farmhouse-style cabinets produced each week ### Tasks: **(a) Objective Function:** Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit. Max \( \square \) **(b) Constraints:** Show the mathematical expression for each of the constraints on the three processes. - Carpentry: \( \square \) - Painting: \( \square \) - Finishing: \( \square \) **(c) Contractual Agreements:** Show the mathematical expression for each of Brooklyn Cabinets’ contractual agreements. - Contemporary: \( \square \) - Farmhouse: \( \square \) By formulating these constraints and the objective function, Brooklyn Cabinets can optimize their weekly production to maximize profit while adhering to operational constraints and contractual agreements.
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