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You are the manager of a donut shop. Presently, you sell your donuts for $1.00 each and everyday you sell 500 donuts. However, you are wondering if you could make a bit more profit by raising the price slightly. Your marketing research shows that for every $0.05 you raise the price, you will sell 10 less donuts. What price would result in the most revenue?

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Solve for:

What price would result in the most revenue?

Step-by-step explanation:

Let the price of one donut = 1 + 0.05x

Let the # of donuts he can sell = 500 - 10x


[tex]R(x) = (1 + 0.05x)(500 - 10x)[/tex]

[tex]R(x) = 500 - 10x + 25x - 0.5x^2[/tex]

[tex]R(x) = -10 + 25-0.5(2x)[/tex]

[tex]= 15-x\\x=15[/tex]

Revenue is maxed when x = 15

When the revenue is maxed,

[tex]Price = 1 + 0.05(15)\\=1 + 0.75\\=1.75[/tex]

Therefore the best price for this scenario is $1.75
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