Explanation Given information: The worker provides 300 h for cutting, 400 h for assembling and 590 h to finish each work. The given table can be redrawn as shown in Table 1. Table Chair Armoire Cutting (h) 1 2 1 1 Assembling (h) 1 2 1 1 2 1 Finishing (h) 1 1 1 2 2 Table 1 Concept used: The inverse of matrix A with 3 × 3 order can be obtained by elementary row operation on a new matrix to change the left side of a matrix in to identity matrix. And automatically the right matrix transformed in to inverse of matrix A . Here, the matrix A is [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] . The new matrix can be written as, [ a 11 a 12 a 13 1 0 0 a 21 a 22 a 23 0 1 0 a 31 a 32 a 33 0 0 1 ] The solution of the matrix equation can be calculated as, A X = B X = A − 1 B Here, A is a square n × n matrix that is invertible, B is known matrix with n rows and X is an unknown matrix. Calculation: Consider x as the number of table, y as the number of chair and z as the number of armoire. Hence they will produce 0.5 x tables, 1 y chair and 1 z of armories. The total production 0.5 x + y + z cutting in all, total hours for cutting is 300 h so the first equation will be 0.5 x + y + z = 300 . The total production 0.5 x + 1.5 y + z cutting in all, total hours for cutting is 400 h so the second equation will be 0.5 x + 1.5 y + z = 400 . The total production x + 1.5 y + 2 z cutting in all, total hours for cutting is 590 h so the third equation will be x + 1

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ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6.1, Problem 73E

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Whether the production of the table, chairs and armories are possible so that all the labor hours will utilize.

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Chapter 6.1, Problem 72E

Chapter 6.1, Problem 74E

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To check: Whether the production of the table, chairs and armories are possible so that all the labor hours will utilize.

Solution Summary: The author explains how the inverse of matrix A with 3times 3 order can be obtained by elementary row operation on a new matrix.

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To check: Whether the production of the table, chairs and armories are possible so that all the labor hours will utilize.

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Chapter 6 Solutions

To check:

Whether the production of the table, chairs and armories are possible so that all the labor hours will utilize.