Here's a hint: if , then
As at the endpoints of the domain and , we know that the maximum profit will be attained at a point where
The question is: A fast food restaurant determines the cost and revenue models for its hamburgers to be:
c = .06X = 7500 ; 0 <= X <= 50000
r= (1/20000)(65000x - x^2) ; 0 <= X <= 50000
a. Write the profit function for this situation
b. determine the intervals the function decreases / increases
c. determine how many hamburgers the restaurant needs to sell to obtain max profit.
I have found the profit function to be p= r-c
so I got : P = (1/20000)(65000x - x^2) - (.6x + 7500)
and P'= (65000x - x^2) + (1/20000)(65000 - x) - .6
but this is not the answer in the book. I'm not sure what I am doing wrong.