What is max profit per day for math problem?

Question

a soft drink vendor analyzes his sales and finds that if he sells x cans of soda in one day his profit is given: F(x)= -0.001x^2+3x-1800

What is max profit per day and how many cans must he sell for max profit?

Answer 1

The maximum point will occur when the first derivative, or slope, goes to zero. So, taking the first derivative you get

F'(x) = -0.002x + 3
Set that equal to zero, and solve for x, which turns out to be 1500

But, do you think this makes any sense? That is, if the vendor sells more than 1500 he loses money? I guess that's possible if the vendor is in a pretty small town. :-)

Answer 2

To find the max, set derivative equal to zero.
So -0.002x + 3 = 0
3 = 0.002x
x = 1500