Exercise 27 Page 162

We will first graph the system, then name the vertices of the overlapping region, which can be also called feasible.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x + y \leq 3 2 x + y \leq 4 x \geq 0, y \geq 0 (I) (II) (III)

Let's start!

To write the equation of the boundary line for the first inequality, we will first isolate the

y -

variable.

x + y \leq 3

$LHS - x \leq RHS - x$

y \leq - x + 3

We can write the equation of the boundary line by changing the inequality symbol to an equals sign.

Inequality : Boundary Line : y \leq - x + 3 y = - x + 3

Since this equation is in slope-intercept form, we can determine its slope

m

and

y -

intercept

b

to draw the line.

Slope - Intercept Form : Boundary Line : y = m x + b y = - 1 x + 3