14. The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant inGreensboro, North Carolina. The plant uses three main resources to make furniture-wood,upholstery, and labor. The resource requirements for each piece of furniture and the totalresources available weekly are as follows:Resource RequirementsWood (board ft.)Upholstery (yd.)Labor (hr.)SofaTable7126.59.Chair4.5Total available resources2,2501,000240The furniture is produced on a weekly basis and stored in a warehouse until the end of the week,when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture. Each sofaearns $400 in profit, each table, $275, and each chair, $190. The company wants to know howmany pieces of each type of furniture to make per week to maximize profit.a. Formulate a linear programming model for this problem.

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Description: 14. The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant inGreensboro, North Carolina. The plant uses three main resources to make furniture-wood,upholstery, and labor. The resource requirements for each piece of

Let number of sofa be x , number of table be y and number of chair be z As the capacity of warehouse…

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14. The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture-wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows: Resource Requirements Wood (board ft.) Upholstery (yd.) Labor (hr.) Sofa 12 Table 5 Chair 4. Total available resources 2,250 1,000 240 The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture. Each sofa earns $400 in profit, each table, $275, and each chair, $190. The company wants to know how many pieces of cach type of furniture to make per week to maximize profit. a. Formulate a linear programming model for this problem.

14. The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture-wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows: Resource Requirements Wood (board ft.) Upholstery (yd.) Labor (hr.) Sofa 12 Table 5 Chair 4. Total available resources 2,250 1,000 240 The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture. Each sofa earns $400 in profit, each table, $275, and each chair, $190. The company wants to know how many pieces of cach type of furniture to make per week to maximize profit. a. Formulate a linear programming model for this problem.

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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14. The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in
Greensboro, North Carolina. The plant uses three main resources to make furniture-wood,
upholstery, and labor. The resource requirements for each piece of furniture and the total
resources available weekly are as follows:
Resource Requirements
Wood (board ft.)
Upholstery (yd.)
Labor (hr.)
Sofa
Table
7
12
6.
5
9.
Chair
4.
5
Total available resources
2,250
1,000
240
The furniture is produced on a weekly basis and stored in a warehouse until the end of the week,
when it is shipped out. The warehouse has a total capacity of 650 pieces of furniture. Each sofa
earns $400 in profit, each table, $275, and each chair, $190. The company wants to know how
many pieces of each type of furniture to make per week to maximize profit.
a. Formulate a linear programming model for this problem.

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