A rental agent estimates that the monthly profit p from a building s stories high is given by p=4600s−100s^
. What height building would she consider most profitable?
To find the height of the building that would result in the most profit, we need to find the value of s that maximizes the profit function p.
First, we need to find the derivative of the profit function with respect to the number of stories, s:
dp/ds = 4600 - 200s
To find the maximum value of p, we set the derivative equal to zero and solve for s:
4600 - 200s = 0
200s = 4600
s = 23
So, a building that is 23 stories high would result in the most profit according to the rental agent's estimate.