Our first step in finding the maximum value of the given equation is to graph the given system and determine the vertices of the overlapping region. Substituting these vertices into the equation, we will find the maximum value.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 6 \leq x + y \leq 13 x \geq 3 y \geq 1 (I) (II) (III)

Inequality I

To graph a compound inequality, we can separate it into two cases.

Compound Inequality : Case I : Case II : 6 \leq x + y \leq 13 6 \leq x + y 6 \leq x + y \leq 13

To make things a bit more simple, we will draw the graph of each case and then combine them.

Case 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 : 6 \leq x + y 6 = x + y

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

6 = x + y

▼

Write in slope-intercept form

SubEqn

$LHS - x = RHS - x$

- x + 6 = y

RearrangeEqn

Rearrange equation

y = - x + 6

Now we can determine the slope

m

and the

y -

intercept

b

of the line.

Slope - Intercept Form : Boundary Line : y = m x + b y = - 1 x + 6

Now that we know the slope and the

y -

intercept, we can use them to draw the boundary line. Note that the boundary line will be solid because the inequality is not strict.

Exercise

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