Chapter 2.6, Problem 5CFU

To determine

To solve: the system of given inequalities by graphing and name the coordinates of the vertices of the polygonal convex set.

Answer to Problem 5CFU

Inequality	$y\ge 0$	$-1<x<7$	$-x+y\le 4$	$x+2y\le 8$
Coordinate Name	x-axis	Between orange	Below Blue line	Below green line

Explanation of Solution

Given information:

  $y\ge 0$... (1)

  $-1<x<7$... (2)

  $-x+y\le 4$... (3)

  $x+2y\le 8$ ... (4)

Calculation:

After rearranging third and fourth inequalities in terms of y , we get

  $\begin{array}{l}y\le 4+x\\ y\le -\frac{1}{2}x+4\end{array}$

Graph for the given inequalities is shown below.

  

Notice that inequality (3) is almost irrelevant to the solution because all points that solve it also solve the inequality (4).

Thus, the coordinate name for the vertices of the polygon set is as follows:

Inequality	$y\ge 0$	$-1<x<7$	$-x+y\le 4$	$x+2y\le 8$
Coordinate Name	x-axis	Between orange	Below Blue line	Below green line