Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Review Exercises - Page 878: 55

Answer

The graph is shown below:
1570277615

Work Step by Step

Let us consider the given inequalities $\begin{align} & y\ge 0 \\ & 3x+2y\ge 4 \\ & x-y\le 3 \\ \end{align}$ Substitute the equals symbol in place of the inequality and rewrite the equation as given below: $\begin{align} & y=0 \\ & 3x+2y=4 \\ & x-y=3 \\ \end{align}$ The first inequality is a horizontal line parallel to the x-axis. Now, take the origin $\left( 0,0 \right)$ as a test point for the equations and check the region in the graph to shade: $\begin{align} & y\ge 0\text{ },\text{ 3}x+2y\ge 4\text{ and }x-y\le 2 \\ & 0\ge 0\text{, }0\ge 4\text{ and }0\le 2 \\ \end{align}$ We see that the first inequality and the third inequality are correct for the test point $\left( 0,0 \right)$; therefore, the shaded region will contain the test point; the second inequality is incorrect, so it will not contain the test point (the origin). We combine these facts to graph the feasible region. The final graph is shown below.
Small 1570277615
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