   Chapter 11.2, Problem 58E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONSCanning Tomato Products Jaeger Foods produces tomato sauce and tomato paste, canned in small, medium, large, and giant-sized cans. The matrix A gives the size (in ounces) of each container. Small Medium Large Giant Ounces [ 6   10   14   28   ] = A The Matrix B tabulates one day’s production of tomato sauce and tomato paste. Cans of sauce Cans of paste SmallMediumLargeGiant [ 2000 2500 3000 1500 2500 1000 1000 500 ] = B (a) Calculate the product A B .(b) Interpret the entries in the product matrix A B .

To determine

(a)

To find:

The product matrix AB.

Explanation

Given:

Jaeger Foods produces tomato sauce and tomato paste, canned in small, medium, large, and giant-sized cans. The matrix A gives the size (in ounces) of each container.

 Small Medium Large Giant Ounces [6  10  14  28  ]=A

The Matrix B tabulates one day’s production of tomato sauce and tomato paste.

 Cans of sauce Cans of paste SmallMediumLargeGiant =B

Approach:

Two matrices A and B can be multiplied if and only if the number of columns in A is same as the number of rows in B.

If A=[aij] is an m×n matrix and B=[bij] an n×k matrix, then their product is the m×k matrix C=[cij], where cij is the inner product of the ith row of A and the jth column of B

To determine

(b)

To find:

The interpretation of the product matrix AB.

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