Linear Programming By: Tyler McKell.

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Presentation transcript:

Linear Programming By: Tyler McKell

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?

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.

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

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?

Graph the Inequalities Sodas Candy

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

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

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