Explanation Given information: A specialty car manufacturer has plants in Auburn, Biloxi, and Chattanooga. Matrix A represents the daily production of car models. On the other hand, matrix B represents the profit per car in January and February. The matrices are A = [ 12 10 0 4 4 20 8 9 12 ] and B = [ $ 1000 $ 500 $ 2000 $ 1200 $ 1500 $ 1000 ] . Concept used: If the matrix A = [ a i j ] is an m × n matrix and B = [ b i j ] as n × r matrix, then the product of the matrix P = [ p i j ] . Here, p i j is the inner product of the i th row of A and j th column of B . Calculation: The order of matrix A is 3 × 3 , matrix B is 3 × 2 The product matrix A B can be calculated if the number of column of matrix A is equal to number of rows of matrix B . Here, the number of column of matrix A is 3 and number of rows of matrix B is 3 . Therefore, the number of column of matrix A is equal to number of rows of matrix B . The product matrix A B can be obtained as, A B = [ 12 10 0 4 4 20 8 9 12 ] [ $ 1000 $ 500 $ 2000 To determine (b) To find: The daily profit in January from the Biloxi plant if all cars were sold. To determine (c) To find: The total daily profit in February from all three plants.

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6.2, Problem 57E

To determine

(a)

To find:

The product matrix AB.

To determine

(b)

To find:

The daily profit in January from the Biloxi plant if all cars were sold.

To determine

(c)

To find:

The total daily profit in February from all three plants.

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Chapter 6.2, Problem 56E

Chapter 6.2, Problem 58E

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(a) To find: The product matrix A B .

Solution Summary: The author explains the product matrix AB, which represents the daily production of car models, and the profit per car in January and February.

Concept explainers

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(a)

To find:

The product matrix AB.

(b)

To find:

The daily profit in January from the Biloxi plant if all cars were sold.

(c)

To find:

The total daily profit in February from all three plants.

Want to see the full answer?

Chapter 6 Solutions

(a) To find: The product matrix A B .

Solution Summary: The author explains the product matrix AB, which represents the daily production of car models, and the profit per car in January and February.

Concept explainers

Videos

(a) To find: The product matrix AB.

(b) To find: The daily profit in January from the Biloxi plant if all cars were sold.

(c) To find: The total daily profit in February from all three plants.

Want to see the full answer?

Chapter 6 Solutions

(a)

To find:

The product matrix AB.

(b)

To find:

The daily profit in January from the Biloxi plant if all cars were sold.

(c)

To find:

The total daily profit in February from all three plants.