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Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426
Textbook Problem

Inventory The Left Coast Bookstore chain discussed in Exercise 39 actually maintained the same sales figures for the first 6 months of the year. Each month, the chain restocked the stores from its warehouse by shipping 600 hardcover, 1,500 softcover, and 1,500 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.

a. Use matrix operations to determine the total sales over the 6 months, broken down by store and type of book.

b. Use matrix operations to determine the inventory in each store at the end of June.

(a)

To determine

To calculate: The inventory in each store at the end of June, where the books in stock at the beginning are shown in the table.

Hard Soft Plastic
San Francisco 1000 2000 5000
Los Angeles 1000 5000 2000

The sales in each month were shown in table as,

Hard Soft Plastic
San Francisco 700 1300 2000
Los Angeles 400 300 500

The restock each month were shown in table as,

Hard Soft Plastic
San Francisco 600 1500 1500
Los Angeles 500 500 500
Explanation

Given Information:

the books in stock at the beginning are shown in the table.

Hard Soft Plastic
San Francisco 1000 2000 5000
Los Angeles 1000 5000 2000

The sales in each month were shown in table as,

Hard Soft Plastic
San Francisco 700 1300 2000
Los Angeles 400 300 500

The restock each month were shown in table as,

Hard Soft Plastic
San Francisco 600 1500 1500
Los Angeles 500 500 500

Calculation:

Consider the table,

Hard Soft Plastic
San Francisco 1000 2000 5000
Los Angeles 1000 5000 2000

Write the table as an inventory matrix.

Thus, inventory is [100020005000100050002000].

Consider, the sales each month were 700 hardcover books, 1300 softcover books and 2000 plastic books in San Francisco and 400 hardcover books, 300 softcover books and 500 plastic books in Los Angeles.

Write the sales in a matrix similar to the inventory matrix.

Thus, sale each month is [70013002000400300500].

Consider, the sales in 6 months is 6 times the sales each month.

Thus, the sales in 6 months is 6×[70013002000400300500].

Consider, 6×[70013002000400300500]

Recall that for any real number n, to calculate nA multiply every element in A by n

(b)

To determine

To calculate: The inventory in each store at the end of June, where the books in stock at the beginning are shown in the table.

Hard Soft Plastic
San Francisco 1000 2000 5000
Los Angeles 1000 5000 2000

The sales in each month were shown in table as,

Hard Soft Plastic
San Francisco 700 1300 2000
Los Angeles 400 300 500

The restock each month were shown in table as,

Hard Soft Plastic
San Francisco 600 1500 1500
Los Angeles 500 500 500

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