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Mathematics

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lys-0071 [83]3 years ago

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Answer:

The function r(x)=(2+.25x)(240-20x) reveals that the revenue earned by the cafe from coffee sales will be $500 after 2 $0.25 price increases.

Step-by-step explanation:

The revenue from sales is the product of the price per cup and the number of cups sold.

For x increases of $0.25 each, the price per cup is (2 +0.25x).

For x increases of $0.25 each, the number of cups sold is (240 -20x).

Then the revenue as a function of x is ...

r(x) = (2 +0.25x)(240 -20x)

The revenue function can be simplified to better show its zeros.

r(x) = 5(8 +x)(12 -x)

The maximum is halfway between the zeros, so is at x = (-8 +12)/2 = 2.

When x=2, the revenue is ...

r(2) = 5(8+2)(12-2) = 5(10)(10) = 500

The function r(x)=(2+.25x)(240-20x) reveals that the revenue earned by the cafe from coffee sales will be $500 after 2 $0.25 price increases.

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