SOLUTION: Please help me with this question. A restaurant decides to add homemade desserts to their menu. When they sell the desserts for $7 each, they sell 80 desserts in a week. When they

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Question 1068413: Please help me with this question.
A restaurant decides to add homemade desserts to their menu. When they sell the desserts for $7 each, they sell 80 desserts in a week. When they raise the price to $9 each, they sell 40 desserts in a week.
a. Write a linear function f(x) that relates x desserts sold to the price f(x) of the desserts.
b. The desserts cost the restaurant $2 each to make. Write a profit function P(x) that gives the total profit for selling x desserts. (Hint: total profit= profit per item times number of items sold)
c. Use your profit function to find the number of desserts that maximizes profit, and then find the price that maximizes profit.
Thank you in advance
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(x,y) for x number of deserts and y price of a desert

Points (80,7) and (40,9).
y=mx+b
b=y-mx
y=%28%289-7%29%2F%2840-80%29%29x%2B%289%2B%281%2F20%2940%29
y=-%281%2F20%29x%2B9%2B2
y=-%281%2F20%29x%2B11

Calling this price function f,
highlight%28f%28x%29=-%281%2F20%29x%2B11%29


SELL x DESERTS
Cost 2x
Revenue x%2Af%28x%29=x%28-%281%2F20%29x%2B11%29=-x%5E2%2F20%2B11x
-
PROFIT FUNCTION P%28x%29=-x%5E2%2F20%2B11x-2x
or simplified,
highlight%28P%28x%29=-x%5E2%2F20%2B9x%29

You can look for the maximum P.