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# Algebra 2 Linear Programming

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## Mace Johnson

on 26 March 2014

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#### Transcript of Algebra 2 Linear Programming

Algebra 2 Linear Programming
Mace Johnson

Cupcakes incorporated is sponsoring an event at the Ohio State Fair selling cupcakes. Two types of cupcakes will be sold. One with sprinkles and one without. It takes two eggs and a half cup of milk to mix the regular cupcakes. Sprinkle cupcakes require two cups of sprinkles, three eggs, and one cup of milk. The company only has 1600 cups of sprinkles and 3000 eggs. The company has to use at least 300 cups of milk to avoid spoiling. It costs five dollars to bake regular cupcakes and five and a half dollars to make sprinkle. The selling price for regular cupcakes is ten dollars and the price for sprinkle cupcakes is twelve dollars. If the company only has \$10,000 and cannot spend more than 3/4 of the money on one type of cupcake, how many batches of each type of cupcake should they make for maximum profit?
Constraints
x= regular cakes
y= sprinkle cupcakes

5x<=7500
5.5y<=7500
x=>0
y=>0
2y<=1600
2x+3y<=3000
1/2x+y=>300
Objective
f(x,y)=5x+6.5y

After subtracting the cost to make the product from the selling price, the objective is found.

Find Maximum profit
Represents spending on 3/4 on more than one type of cupcake
Cannot make a negative quantity
Only 1600 cups of sprinkles available
Only 3000 eggs available
Must use at least 300 cups on milk
Graph
Plug in points of intersection for maximum profit!
F(x,y)=5(1500)+ 5.5(0) = 7500 MAXIMUM PROFIT
F(x,y)=5(300)+ 5.5(800) = 6700
F(x,y)=5(0)+ 5.5(800) = 5200
F(x,y)=5(600)+ 5.5(0) = 3000
F(x,y)=5(0)+ 5.5(300) = 1950 MINIMUM PROFIT
Conclusion
To make the most money from cupcakes, Cupcakes Incorporated needs to bake 1500 batches of regular cupcakes and 0 batches of sprinkles for a maximum profit of \$7500.00
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