(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.

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Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style
cabinets sell for $130 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
Max
Hours per Process
Carpentry Painting Finishing
2.3-
2,7
1.5
1.1
1.3
1.3
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 2,800 in
carpentry, 1,400 in painting, and 1,400 in finishing.
Brooklyn also has a contract that requires the company to supply one of its customers with 450 contemporary cabinets and 725 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.
(b) Show the mathematical expression for each of the constraints on the three processes.
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 $130 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 Max Hours per Process Carpentry Painting Finishing 2.3- 2,7 1.5 1.1 1.3 1.3 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 2,800 in carpentry, 1,400 in painting, and 1,400 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 450 contemporary cabinets and 725 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. (b) Show the mathematical expression for each of the constraints on the three processes.
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