2-7 Linear Programming Pre Calc A.

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2-7 Linear Programming Pre Calc A

Vocabulary Feasible Region Constraints Minimum maximum

Steps to Solve Linear Programming Problems Define variables Write the profit equation Write the constraints as a system of inequalities Graph the system Find the coordinates of the vertices of the feasible region Substitute coordinates into the profit equation Find the minimum and maximum

Ex 17: Myra’s candy factory packages bags of mixed nuts. Myra has 75 lbs of cashews and 120 lbs of peanuts. They are to be mixed in 1 lb packages in the following way: a low grade package contains 4 oz of cashews and 12 oz of peanuts and a high grade package contains 8 oz of peanuts and 8 oz of cashews. A profit of $0.35 per package will be made on the low grade mixture and a profit of $0.55 will be made on the high grade mixture. How many packages of each mixture should Myra make to obtain maximum profit?

Ex 17 cont: x = y = P(x) = Constraints: Low grade Mix High Grade Mix Maximum available Cashews Peanuts

Graph

Find the minimum and maximum (x, y) .35x + .55y P(x, y) Final answer: