Explanation Given Information: The Left Coast Bookstore chain in January sold 700 hardcover books, 1300 soft cover books, and 2000 plastic books in San Francisco; it sold 400 hardcover, 300 softcover and 500 plastic books in Los Angeles. Each hardcover book costs the stores $ 10 and each softcover book costs $ 5 and each plastic book costs $ 10 . Formula Used: Multiplication of Matrices: If A is an m × n matrix and B is an n × k matrix, then the product A B is the m × k matrix whose i j th entry is the product ( A B ) i j = [ a i 1 a i 2 a l i 3 ... a i n ] [ b 1 j b 2 j b 3 j . . . b n j ] = a i 1 b 1 j + a i 2 b 2 j + a i 3 b 3 j + ... + a i n b n j Calculation: It is provided that each hardcover book costs the stores $ 10 , each softcover book costs $ 5 , and each plastic book costs $ 10 . The Left Coast Bookstore chain in January sold 700 hardcover books, 1300 soft cover books, and 2000 plastic books in San Francisco. Total number of sold hardcover is 400 and 300 softcover, and 500 plastic books in Los Angeles and books sell for $ 30 each, softcover books sell for $ 10 each, and plastic books sell for $ 15 each. Three prices and three quantities are provided. So, first form two matrices, one row and one column as: The price matrix (row matrix) can be constructed as: P = [ 30 10 15 ] The cost matrix is constructed as: C = [ 10 5 10 ] For the quantity matrix, two types of quantities are provided. So, the matrix will be of the order 2 × 3 where the first row will represent the books sold in San Francisco, and the second row will represent the books sold in Los Angeles. The Quantity matrix can be constructed as: Q = [ 700 1300 2000 400 300 500 ] Now, Profit can be calculated as: Profit = Revenue − Cost This can also be written as: Profit = Q P − Q C = Q ( P − C ) Substitute the respective matrices: Profit = [ 700 1300 2000 400 300 500 ] { [ 30 10 15 ] − [ 10 5 10 ] } =

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 4.2, Problem 58E

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To calculate: The total profit at each store in January using matrix operations if each hardcover book costs the stores $10 and each softcover book costs $5 and each plastic book costs $10.

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Chapter 4.2, Problem 57E

Chapter 4.2, Problem 59E

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The total profit at each store in January using matrix operations if each hardcover book costs the stores $ 10 and each softcover book costs $ 5 and each plastic book costs $ 10 .

Solution Summary: The author calculates the total profit of the books sold in San Francisco and Los Angeles using matrix operations.

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To calculate: The total profit at each store in January using matrix operations if each hardcover book costs the stores $10 and each softcover book costs $5 and each plastic book costs $10.

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