Question

A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover, softcover, and plastic (for infants). At the beginning of January, the central computer showed the following books in stock.Hard Soft PlasticSan Francisco 1,000 3,000 6,000Los Angeles 1,000 6,000 3,000Its sales in January were as follows: 600 hardcover books, 1,300 softcover books, and 2,000 plastic books sold in San Francisco, and 400 hardcover, 300 softcover, and 400 plastic books sold in Los Angeles. The bookstore chain 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 500 hardcover, 1,400 softcover, and 1,400 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.Hard Soft PlasticSan Francisco Los Angeles (b) Use matrix operations to determine the inventory in each store at the end of June.Hard Soft PlasticSan Francisco Los Angeles

Answer 1

Answer:A. 3,600 hard cover, 7,800 soft cover and 12,000 plastic cover books will be sold in San Francisco and 2,400 hard cover, 1,800 soft cover and 2,400 plastic cover books will be sold in Los Angeles.

B.400 hard cover, 3,600 soft cover and 2,400 plastic cover books will be left over in San Francisco and 1,600 hard cover, 7,200 soft cover and 3,600 plastic cover books will be left over in Los Angeles.

Step-by-step explanation:

Let the First column of the matrix represent hard cover books, the second represent soft cover books and the third represents plastic cover books

For the rows, let the first row represent the store in San Francisco and the second row, the store in Los Angeles;

To determine the sales using matrix operations

The matrix representing the sales is;

( The matrices are attached down below)

The sales for 6months will be

3,600 hard cover, 7,800 soft cover and 12,000 plastic cover books will be sold in San Francisco and 2,400 hard cover, 1,800 soft cover and 2,400 plastic cover books will be sold in Los Angeles.

Using Matrix operations, the total inventory at the end of 6 months will be;

Total inventory at the end of 6 months = Stock at the beginning of January + (6*stocks during the months) - (Total sales)

=400 hard cover, 3,600 soft cover and 2,400 plastic cover books will be left over in San Francisco and 1,600 hard cover, 7,200 soft cover and 3,600 plastic cover books will be left over in Los Angeles.