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Warm-Up Graph the following system of inequalities. Find the coordinates at each vertices.

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Linear Programming 1.4-1.7 Test: Oct. 30

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Vocabulary Linear programming: maximizing/minimizing a linear objective function. Objective function: gives quantity that is to maximized or minimized and subject to constraints Constraints: boundaries of a function Feasible region: solution area shaded when all constraints are graphed –If bounded (definite shape) then it has a max./min. –The max./min are the vertices.

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Find the minimum value and the maximum value of the objective function C=3x+2y subject to the following constraints.

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Find the minimum value and the maximum value of the objective function C= 4x + 3y subject to the following constraints. Min.: 0 Max.: 32

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Find the minimum value and the maximum value of the objective function C= 7x + 5y subject to the following constraints. Min.: 14, Max.: 44

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Find the minimum value and the maximum value of the objective function C= 2x + 8y subject to the following constraints. Min.: 0, Max.: 56

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Linear Programming *Word Problems* 1.4-1.7 Test: FRIDAY!

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A small company produces knitted afghans and sweaters and sells them through a chain of specialty stores. The company is to supply the stores with a total of no more than 100 afghans and sweaters per day. The stores guarantee that they will sell at least 10 and no more than 60 afghans per day and at least 20 sweaters per day. The company makes a profit of $10 on each afghan and a profit of $12 of each sweater. How many of each should they provide to maximize their profit?

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You are taking a test in which items of type A are worth 10 points and items of type B are worth 15 points. It takes 3 minutes to answer each item of type A and 6 minutes for each item of type B. The total time allowed is 60 minutes, and you may not answer more than 16 questions. Assuming all of your answers are correct, how many items of each should you answer to get the highest score?

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A man plans to invest up to $22,000 in bank X or bank Y, or both. He will invest at least $2000, but no more than $14,000, in bank X. He will invest no more than $15,000 in bank Y. Bank X pays 6% simple interest, and bank Y pays 6.5%. How much should he invest in each to maximize income? What is the maximum income?

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Homework Wagons are sold at a craft fair. It takes 4 hours to make a small one and 6 hours to make a large one. The owner will make a profit of $12 for a small wagon and $20 for a large one. He has no more than 60 hours available to make the wagons and wants to have at least 6 small wagons to sell. How many of each size should be made to maximize the profit?

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