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Linear Programming Objective: I can solve problems using linear programming.

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Constraints: Inequalities Feasible region: All points that satisfy the constraints Objective Function: Quantity you want to maximize or minimize Vertices of feasible region will be maximum or minimum Linear Programming: Method for finding a minimum or maximum of some quantity given constraints

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Maximum Minimum Objective Function: Find the maximum or minimum points Vertices: (0, 0) (2, 0) (4, 2) (0, 4) Test Vertices 2(0) + 0 = 0 2(2) + 0 = 4 2(4) + 2 = 10 2(0) + 4 = 4

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Total 10x Minutes to work Number Cost Profit x 4x4x 6x6x 30y y 20y 22y 50 20(60) = 1200 600 ≤ ≤ ≥ Maximize T-Shirts 10 minutes to make Supplies cost $4 Profit $6 Sweatshirts 30 minutes to make Supplies cost $20 Profit $22 Sweatshirts (y) T-Shirts (x) You are printing T-shirts and sweatshirts to sell before homecoming. You have at most 20 hours to work. You can spend no more than $600 and you must sell at least 50 items. + + + +

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Maximum T-Shirts (x)Sweatshirts (y)Total Minutes to work10x30y≤ 1200 Cost4x4x20y≤ 600 Numberxy≥ 50 Profit6x6x22ymaximize 3006(50)+22(0) = ( 50, 0) 700 6(25)+22(25) = (25, 25) 780 6(75)+22(15) = (75, 15) 720 6(120)+22(0) =(120, 0) Pg. 160 #10-13 75 T-shirts, 15 Sweatshirts Vertices: Test Vertices + + + +

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Paying for College You have been given $40,000 to invest for a college scholarship. You must invest in both stocks and bonds. Let x represent the dollars invested in stocks. Let y represent the dollars invested in bonds. What inequality can you write to represent the amount of money invested in stocks and bonds? Stocks Bon ds

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Paying for College Each investment requires a minimum purchase of $5,000 What are your new inequalities? Since stocks are more risky you want to at least twice as many bonds as stocks. What is the inequality? Stocks Feasible Region Bon ds Constraints Pg 339 #1-3, 5

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