Chapter 7.5, Problem 63E

To determine

To sketch: the graph for the system of inequalities that describes the various amounts that can be deposited in each account.

Explanation of Solution

Given:

A person plans to invest up to $20000 in two different interest bearing accounts. Each account must contain at least $5000. The amount in one account is to be at least twice the amount in the other account.

Calculation:

Consider the amount in the smaller account and larger account be $x$and $y$respectively.

Since, each account is to contain at least $5000.

  $\begin{array}{l}x\ge 5000\\ y\ge 5000\end{array}$

The total amount in the two accounts should be at most $20000.

  $x+y\le 20000$

The amount in the larger account should be at least twice the amount in the smaller account.

  $y\ge 2x$

The system of inequalities can be written as,

  $\begin{array}{l}x+y\le 20000\\ y\ge 2x\\ x\ge 5000\\ y\ge 5000\end{array}$

The graph of the system of inequalities is shown below.