Question

Select the correct option from each drop-down menu.

Sully manages a cafe that typically sells 240 cups of coffee per day for $2 each. Sully knows that for each $0.25 increase in the price of coffee, 20 fewer cups of coffee will be sold. Let x represent the number of $0.25 price increases and f(x) represent the total revenue earned from coffee sales.

Sully wants to write an equation in the form that reveals the best potential earnings for the cafe in terms of revenue earned from coffee sales each day.

Complete the following statement for this situation.


The function
reveals that the
revenue earned by the cafe from coffee sales will be $
after
$0.25 price increases.

Answer 1

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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.

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 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.