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


The graph is shown below:

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.
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