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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

4. Linear Programming

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Exercise 11 Page 160

Graph the given system and determine the vertices of the overlapping region. Substituting these vertices into the equation will help you find the minimum value.

Graph:

Vertices: $(8, 0),$ $(2, 3)$
Minimum: $8$ at $(8, 0)$

Practice makes perfect

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 minimum value.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x + 2 y \geq 8 x \geq 2 y \geq 0 (I) (II) (III)

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 + 2 y \geq 8 x + 2 y = 8

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

x + 2 y = 8

▼

Write in slope-intercept form

$LHS - x = RHS - x$

2 y = - x + 8

$LHS / 2 = RHS / 2$

y = - \frac{1}{2} x + 4

Now we can determine the slope

m

and the

y -

b

of the line.

Slope - Intercept Form : Boundary Line : y = m x + b y = - \frac{1}{2} x + 4

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Subchapter links

Lesson Check p.160

Practice and Problem-Solving Exercises p.160-162

Standardized Test Prep p.162

Mixed Review p.162