Chapter 7.5, Problem 66E

To determine

To sketch: the graph of inequalities that describes all possible inventory levels.

Explanation of Solution

Given information:

A store sells two models of laptop computers. The store stocks at least twice as many units of model A as of model B. The costs to the store for the two model are $800 and $1200, respectively. The management does not want more than $20000 in computer inventory at any one time, and it wants at least four model A laptop computers and two model B laptop computers in inventory at all times.

Calculation:

Let

  $A\ge 2B$

Since, the cost of A and B per piece is $800 and $1200 respectively.

  $800A+1200B\le 20000$

As per the minimum stock condition,

  $\begin{array}{l}A\ge 4\\ B\ge 2\end{array}$

The very first inequality has greater than equal to symbol so it will be away from the origin, the second one is less then equal to so it will be owards the origin, the third and fourth inequality region will also be away from the origin and the region representing the above inequalities will look like below,

  

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