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**CB Radios Linear Programming**

By: Tai Parker & Brittany Walker

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A manufacturer of CB radios makes a profit of $25 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 200 radios. How many of each type should be produced daily in order to maximize the profit?

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**(Objective Function) Maximum Profit = 25x+30y**

X = deluxe models Y = standard models Constraints X ≥ 80 Y ≥ 100 X + Y ≤ 200

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**Y ≥ 100 X ≥ 80 X + Y ≤ 200 Standard models and Deluxe Models Profit**

(80,120) Standard Models (80,100) (100,100) Deluxe Models

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**Finding the Maximum P=25X+30Y The maximum is $5600**

25(80)+30(100)= 5000 25(80)+30(120)= 5600 25(100)+30(100)= 5500 The maximum is $5600 (80,120)

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Summary For the optimum profit 80 deluxe models and 120 standard models should be produced per day. This was found by creating a graph and graphing constraints the company gave, for a maximum profit of $5600.

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