SOLUTION: A campground charges $20.00 to camp for one night. They average 56 people each night. A recent survey indicated that for every $1.00 decrease in the nightly price, the number of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A campground charges $20.00 to camp for one night. They average 56 people each night. A recent survey indicated that for every $1.00 decrease in the nightly price, the number of       Log On


   

Question 1160001: A campground charges $20.00 to camp for one night. They average 56 people each night. A recent survey indicated that for every $1.00 decrease in the nightly price, the number of camping sites rented increases by 7.
Create a Revenue equation.

What price will maximize nightly revenue? Show the steps of your solution.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=number of $ decrease in price and increased number of rentals by 7
(20-x)(56+7x)=1120+84x-7x^2, which is the revenue function.
maximum is where x=-b/2a=-84/-14=6
so revenue is maximized with 56+42=98 rentals paying $20-$6=$14 a night, or $1372.
the price should be $14 to maximize revenue.
graph%28300%2C300%2C-10%2C10%2C-50%2C1500%2C-7x%5E2%2B84x%2B1120%29