Chapter 7.5, Problem 67E

To determine

To find:

The all possible production levels and draw the graph of the solution set of the system of inequalities

Answer to Problem 67E

  $\begin{array}{l}x+y\le 20,000\\ y\ge 2x\\ x\ge 5000\\ y\ge 5000\end{array}$

Explanation of Solution

Given:

The equation

  $\begin{array}{l}x+y\le 20,000\\ y\ge 2x\\ x\ge 5000\\ y\ge 5000\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

Total investment up to $\$20000$

  $x+y\le 20,000$

Each account must be atleast $\$5000$

  $x\ge 5000$

Each account must be atleast $\$5000$

  $y\ge 5000$

Amount in one account must be at least twice the other account

  $y\ge 2x$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

  $\begin{array}{l}x+y\le 20,000\\ y\ge 2x\\ x\ge 5000\\ y\ge 5000\end{array}$

Draw the table

$x-axis$	$5000$	$6666.67$	$0$	$5000$
$y-axis$	$10000$	$13,333$	$20000$	$0$

Draw the graph