Chapter 4.1, Problem 40E

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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

Consider, the sales each month were

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

Thus, sale each month is

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

Thus, the sales in 6 months is

Consider,

Recall that for any real number *n*, to calculate *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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