Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $110 and farmhouse-style cabinets sell for $120. 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. Style Contemporary Farmhouse Hours per Process Carpentry 2.2 2.6 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 2,600 in carpentry, 1,300 in painting, and 1,300 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 475 contemporary cabinets and 675 farmhouse-style cabinets each week. Define x and y as follows. Painting Finishing 1.5 1.3 1.2 1.4 • x = the number of contemporary-style cabinets produced each week • y = the number of farmhouse-style cabinets produced each week carpentry painting finishing (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. contemporary farmhouse (c) Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements.
Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $110 and farmhouse-style cabinets sell for $120. 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. Style Contemporary Farmhouse Hours per Process Carpentry 2.2 2.6 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 2,600 in carpentry, 1,300 in painting, and 1,300 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 475 contemporary cabinets and 675 farmhouse-style cabinets each week. Define x and y as follows. Painting Finishing 1.5 1.3 1.2 1.4 • x = the number of contemporary-style cabinets produced each week • y = the number of farmhouse-style cabinets produced each week carpentry painting finishing (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. contemporary farmhouse (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.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:Brooklyn Cabinets is a manufacturer of kitchen cabinets.
The two cabinetry styles manufactured by Brooklyn are
contemporary and farmhouse. Contemporary-style
cabinets sell for $110 and farmhouse-style cabinets sell
for $120. 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
Contemporary
Farmhouse
Carpentry Painting Finishing
2.2
1.5
1.3
2.6
1.2
1.4
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 2,600 in
carpentry, 1,300 in painting, and 1,300 in finishing.
Brooklyn also has a contract that requires the company
to supply one of its customers with 475 contemporary
cabinets and 675 farmhouse-style cabinets each week.
Define x and y as follows.
• 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
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