04/21/23 Perkins

Honors Precalculus

Day 10Sections 10.8 and 10.9

Graphing Inequalities

Graph the solution set for 2 4x y 2 1y x 2 4y x

12 2y x 2

-2

shade below

shade above

Shade aboveShade below

(-2,3)

(1.5,1.25)

On your calculator: Move the cursor to the left of y1 and use the enter key to change its symbol.

The INTERSECT function will still find intersection points.

Linear Programming

A nutrition center sells health food to mountain climbing teams. The Trailblazer Mix contains one pound of corn cereal mixed with four pounds of wheat cereal and sells for $9.75. The Frontier Mix contains two pounds of corn cereal mixed with three pounds of wheat cereal and sells for $9.50. The center has 60 pounds of corn cereal and 120 pounds of wheat cereal available. How many packages of each mix should be sold for the center to maximize its income? What is its maximum income?

What are we really trying to do?

maximize income

What are the limitations/constraints?

corn

wheat

income 9.75 9.50x y

2 60x y

4 3 120x y

x = trailblazer mixy = frontier mix

12 30y x 43 40y x

x and y must not be less than zero!

2 graphing options

80

60

40

20

20 40 60 80

Shade the solution set Shade everything but the solution set

The vertices of the region created by the solution set are the

potential solutions.

y-interceptCALC:VALUE:0

Be sure you use the correct line!

(0,0)

(0,30) (30,0) x-interceptCALC:ZERO

Be sure you use the correct line!

intersectionCALC:INTERSECT

(12,24)

Test each vertex in the income equation to find the

maximum:

income 9.75 9.50x y

(0,30)

(0,0) (12,24)

(30,0)

income $0income $285

income $345income $292.50

The center should sell 12 Trailblazer and 24 Frontier for a maximum income of $345.

Perkins

Honors Precalculus

Day 10Sections 10.8 and 10.9

Graphing Inequalities

Graph the solution set for 2 4x y 2 1y x

2

-2

On your calculator:

Linear Programming

A nutrition center sells health food to mountain climbing teams. The Trailblazer Mix contains one pound of corn cereal mixed with four pounds of wheat cereal and sells for $9.75. The Frontier Mix contains two pounds of corn cereal mixed with three pounds of wheat cereal and sells for $9.50. The center has 60 pounds of corn cereal and 120 pounds of wheat cereal available. How many packages of each mix should be sold for the center to maximize its income? What is its maximum income?

What are we really trying to do?

What are the limitations/constraints?

2 graphing options

80

60

40

20

20 40 60 80

The vertices of the region created by the solution set are the

potential solutions.