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 Plastic
San Francisco 1,000 2,000 6,000
Los Angeles 1,000 6,000 2,000
Its sales in January were as follows: 600 hardcover books, 1,200 softcover books, and 1,900 plastic books sold in San Francisco, and 300 hardcover, 200 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 600 hardcover, 600 softcover, and 600 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 Plastic
San Francisco
Los Angeles
(b) Use matrix operations to determine the inventory in each store at the end of June.
Hard Soft Plastic
San Francisco
Los Angeles

Answer 1

a. Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 3,600 7,200 11,400

Los Angeles 1,800 1,200 2,400

b) Ending Inventory: Matrix D:

Hard Soft Plastic

San Francisco 400 3,200 3,000

Los Angeles 2,800 8,400 3,200

Explanation:

a) Data and Calculations:

Stock on January 1: Matrix A

Hard Soft Plastic

San Francisco 1,000 2,000 6,000

Los Angeles 1,000 6,000 2,000

Sales in January: Matrix B

Hard Soft Plastic

San Francisco 600 1,200 1,900

Los Angeles 300 200 400

Restocking: Matrix C

Hard Soft Plastic

San Francisco 500 1,400 1,400

Los Angeles 600 600 600

Total Sales over the first 6 months =

Matrix B * 6 = Matrix B6

Sales in January: Matrix B

Hard Soft Plastic

San Francisco 600 1,200 1,900

Los Angeles 300 200 400

* 6

=

Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 3,600 7,200 11,400

Los Angeles 1,800 1,200 2,400

Matrix C6 = Matrix C * 6

=

Restocking: Matrix C6

Hard Soft Plastic

San Francisco 3,000 8,400 8,400

Los Angeles 3,600 3,600 3,600

Inventory at the end of June =

Matrix A + Matrix C6 - Matrix B6

= Matrix D

Stock on January 1: Matrix A

Hard Soft Plastic

San Francisco 1,000 2,000 6,000

Los Angeles 1,000 6,000 2,000

+

Restocking: Matrix C6

Hard Soft Plastic

San Francisco 3,000 8,400 8,400

Los Angeles 3,600 3,600 3,600

-

Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 3,600 7,200 11,400

Los Angeles 1,800 1,200 2,400

Ending Inventory: Matrix D:

Hard Soft Plastic

San Francisco 400 3,200 3,000

Los Angeles 2,800 8,400 3,200