1. Linear Programming
By: Tyler McKell

2. The Situation
John, Lisa, and Rebecca are selling candy bars and sodas to raise money for a class trip. They have $200 to spend. Each pack of 10 candy bars will cost $5.00. Each six-pack of soda will cost $3.60. The number of six packs of sodas should not be more than the number of 10 packs of candy bars. They can sell each pack of candy for $10.00 and each six-pack of soda for $8.00. How many packs of candy bars and six-packs of soda should they purchase?

3. The 6 Steps for Linear Programming
Identify the variables
Write the inequalities
Graph the inequalities
Identify the corner points
Determine the objective equation
Test the corner points in the objective equation to find the minimum or maximum.

4. Identify the Variables
John, Lisa, and Rebecca are selling candy bars and sodas to raise money for a class trip. They have $200 to spend. Each pack of 10 candy bars will cost $5.00. Each six-pack of soda will cost $3.60. The number of six packs of sodas should not be more than the number of 10 packs of candy bars. They can sell each pack of candy for $10.00 and each six-pack of soda for $8.00. How many packs of candy bars and six-packs of soda should they purchase?
Candy Bars – C Sodas – S

5. Write the inequalities
John, Lisa, and Rebecca are selling candy bars and sodas to raise money for a class trip. They have $200 to spend. Each pack of 10 candy bars will cost $5.00. Each six-pack of soda will cost $3.60. The number of six packs of soda should not be more than the number of 10 packs of candy bars. They can sell each pack of candy for $10.00 and each six-pack of soda for $8.00. How many packs of candy bars and six-packs of soda should they purchase?

6. Graph the Inequalities
Sodas
Candy

7. Identify the Corner Points
Sodas
(26.26,23.26)
(0,0)
(40,0)
Candy

8. Determine the Objective Equation
John, Lisa, and Rebecca are selling candy bars and sodas to raise money for a class trip. They have $200 to spend. Each pack of 10 candy bars will cost $5.00. Each six-pack of soda will cost $3.60. The number of sodas should not be more than twice the number of candy bars. They can sell each pack of candy for $10.00 and each six-pack of soda for $8.00. How many packs of candy bars and six-packs of soda should they purchase?
Profit = 10C + 8S

9. Test the Corner Points in the Objective Equation
Profit P = 10C + 8S
(0,0)
10(0) + 8(0) = 0
(40,0)
10(40) + 8(0) = 400
(26, 23)
10(26) + 8(23) = 444
The maximum profit is $444.00