SOLUTION: A food truck sells 100 hot dogs each day when it charges $2.00 per hot dog. For a $0.25 decrease in price, the food truck sells 25 more hot dogs.
a. How much should the food tr
Question 1120089: A food truck sells 100 hot dogs each day when it charges $2.00 per hot dog. For a $0.25 decrease in price, the food truck sells 25 more hot dogs.
a. How much should the food truck charge to maximize daily revenue? Answer by ikleyn(52803) (Show Source):
An equivalent rephrasing is "for each decrease the price in 1 cent the number of sold hot dogs increases in 1", or
in the Math term, at the price 200-n cents the number of sold hot dogs is 100+n.
Then the revenue is R(n) = (100+n)*(200-n) = 20000 + 200n - 100n - n^2 = -n^2 + 100n + 20000.
And the problem asks to find the maximum of the quadratic form R(n).
The maximum is achieved at n = = 50.
Anser. The food truck should charge 200-50 = 150 cents = $1.50 per hot dog.
