Exercise 6 Page 160

We will first graph each inequality separately, then combine the graphs. Next, we will name the vertices of the overlapping region, which can be also called feasible.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x + y \leq 8 y \geq 5 x \geq 0 (I) (II) (III)

Let's start!

Inequality I

To graph an inequality, we first determine its boundary line. By changing the inequality symbol to an equals sign, the boundary line can be determined.

Inequality : Boundary Line : x + y \leq 8 x + y = 8

Since the boundary line is not in slope-intercept form, we will rewrite it in slope-intercept form.

x + y = 8

SubEqn

$LHS - x = RHS - x$

y = - x + 8