A juice company makes two kinds of juice: Orangeade and Berry-Fruity. One gallon

Question

A juice company makes two kinds of juice: Orangeade and Berry-Fruity. One gallon of Orangeade is made by mixing 2.5 quarts of orange juice and 1.5 quarts of raspberry juice, while one gallon of berry-fruity is made by mixing 3 quarts of raspberry juice and 1 quart of orange juice. A profit of $.50 is made on every gallon of Orangeade sold, and a profit of $.40 is made on every gallon of Berry-fruity sold. If the company has 150 gallons of raspberry juice and 125 gallons of organge juice on hand, how many gallons of each type of juice should be made to maximize profit?

Explanation / Answer

1.5x + 3y <= 150 [raspberry juice constraint] 4. Graph your constraints y <= -2.5x + 125 y <= -0.5x + 50 5. Once graphed, you will see that there are three points of intersection (0,50) (50,0) (37.5,31.25) 6. Use these points to evaluate the profit function to see which gives max profit P(x,y) = 0.5x + 0.4y P(0,50) = 0.5(0) + 0.4(50) = 20 P(50,0) = 0.5(50) + 0.4(0) = 25 P(37.5,31.25) = 0.5(37.5) + 0.4(31.25) = 31.25 So producing 37.5 gallons of orangeade and 31.25 gallons of berry-fruity gives us the max profit of $31.25

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