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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 12 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 maximum value.

Graph:

Vertices: $(2, 1),$ $(2, 5),$ $(3, 5),$ $(6, 2),$ $(6, 1)$
Maximum: $22$ at $(6, 2)$

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 maximum value.

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 2 \leq x \leq 6 1 \leq y \leq 5 x + y \leq 8 (I) (II) (III)

Inequality I

The first inequality contains only the

x -

variable.

2 \leq x \leq 6 ⇕ x \geq 2 and x \leq 6

This compound inequality describes all values of

x

that are greater than or equal to

2

and less than or equal to

6 .

This means that all coordinate pairs with an

x -

coordinate that is greater than or equal to

2

and less than or equal to

6

will be in the solution set. Note that both inequalities are non-strict, so the boundary lines will be solid.

Inequality II

We will follow a similar process for the second inequality. However, this time the inequality contains only the

y -

variable.

1 \leq y \leq 5 ⇕ y g e q 1 and y \leq 5

Subchapter links

Lesson Check p.160

Practice and Problem-Solving Exercises p.160-162

Standardized Test Prep p.162

Mixed Review p.162