   Chapter 11.2, Problem 59E ### 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

# APPLICATIONSProduce Sales A farmer’s three children, Amy, Beth, and Chad, run three roadside produce stands during the summer months. One weekend they all sell watermelons, yellow squash, and tomatoes. The matrices A and B tabulate the number of pounds of each product sold by each sibling on Saturday and Sunday. Saturday Melons Squash Tomatoes AmyBethChad [ 120   50   60   40   25   30 60   30   20     ] = A Sunday Melons Squash Tomatoes AmyBethChad [ 100   60   30   35   20   20 60   25   30     ] = B The Matrix C gives the price per pound (in dollars) for each type of produce that they sell. Price per pound AmyBethChad [ 0.10 0.50 1.00 ] = C Perform each of the following matrix operations, and interpret the entries in each result. (a) A C (b) B C (c) A + B (d) ( A + B ) C

To determine

(a)

To find:

The result of the matrix operation AC and interpret the result.

Explanation

Given:

A farmer’s three children, Amy, Beth, and Chad, run three roadside produce stands during the summer months. One weekend they all sell watermelons, yellow squash, and tomatoes. The matrices A and B tabulate the number of pounds of each product sold by each sibling on Saturday and Sunday.

 Saturday Melons Squash Tomatoes AmyBethChad [120 50 60 40 25 3060 30 20  ] =A Sunday Melons Squash Tomatoes AmyBethChad [100 60 30 35 20 2060 25 30  ] =B

The Matrix C gives the price per pound (in dollars) for each type of produce that they sell.

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.

Calculations:

Consider the matrix operation AC and the given matrices A= and C=[0

To determine

(b)

To find:

The result of the matrix operation BC and interpret the result.

To determine

(c)

To find:

The result of the matrix operation A+B and interpret the result.

To determine

(d)

To find:

The result of the matrix operation (A+B)C and interpret the result.

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