   Chapter 11.2, Problem 56E ### 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

# APPLICATIONSFact-Food Sales A small fast-food chain with restaurants in Santa Monica, Lang Beach, and Anaheim sells only hamburgers, hot dogs, and milk shakes. On a certain day, sales were distributed according to the following matrix. Number of items sold Santa Monica Long Beach Anaheim HamburgersHot dogsMilk shakes [ 4000 1000 3500 400 300 200 700 500 9000 ] = A The price of each item is given by the following matrix. Hamburger Hot Dog Milk shake [ $0.90$ 0.80 $1.10 ] = B (a) Calculate the product B A .(b) Interpret the entries in the product matrix B A . To determine (a) To find: The product matrix BA. Explanation Given: A small fast-food chain with restaurants in Santa Monica, Lang Beach, and Anaheim sells only hamburgers, hot dogs, and milk shakes. On a certain day, sales were distributed according to the following matrix.  Number of items sold Santa Monica Long Beach Anaheim HamburgersHot dogsMilk shakes  =A The price of each item is given by the following matrix.  Hamburger Hot Dog Milk shake [$0.90$0.80$1.10] =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.

Calculations:

Consider the matrix operation BA and the given matrices A= and B=[\$0

To determine

(b)

To find:

The interpretation of the product matrix BA.

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