Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured 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. The objective function is maximize b. Show the mathematical expression for each of the constraints on the three processes. Hours available in carpentry: X1 + Hours available in painting: x2 + Y2 s Hours available in finishing: X3 +
Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured 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. The objective function is maximize b. Show the mathematical expression for each of the constraints on the three processes. Hours available in carpentry: X1 + Hours available in painting: x2 + Y2 s Hours available in finishing: X3 +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 $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.
The objective function is maximize
b. Show the mathematical expression for each of the constraints on the three processes.
Hours available in carpentry:
X1 +
Hours available in painting:
X2 +
Y2 s
Hours available in finishing:
Хз +
Y3 S
Transcribed Image Text:c. Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements.
00
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