A factory manufacturesa chairs and tables, each requiring the use of three operations: Cutting, assembly, and finishing. The first operation can be used at most 40 hours: the second at most 42 hours: and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing: a table needs 2 hours of cutting: 1 hour of assembly: and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 a unit for a table, how many units of each should be manufactured to maximize profit?
A factory manufacturesa chairs and tables, each requiring the use of three operations: Cutting, assembly, and finishing. The first operation can be used at most 40 hours: the second at most 42 hours: and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing: a table needs 2 hours of cutting: 1 hour of assembly: and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 a unit for a table, how many units of each should be manufactured to maximize profit?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.1: Solution Of Linear Systems
Problem 56E
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Question
A factory manufacturesa chairs and tables, each requiring the use of three operations: Cutting, assembly, and finishing. The first operation can be used at most 40 hours: the second at most 42 hours: and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing: a table needs 2 hours of cutting: 1 hour of assembly: and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 a unit for a table, how many units of each should be manufactured to maximize profit?
Expert Solution
Step 1: Given.
Given: The given information is listed in the table below:
| Chairs | Tables | Availability | |
| Cutting hours | 1 | 2 | |
| Assembly hours | 2 | 1 | |
| Finishing hours | 1 | 1 | |
| Profit(in dollar) | 20 | 30 | Maximize |
To find: How many units of each should be manufactured to maximize profit?
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