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