Math question help ?
The profit function for a certain medication can be modeled by the equation: P(s)=-25s^2+1300s-11560
where P is profit and s is selling price.
a) According to the model, what selling price will yield the highest profit?
b) What is the maximum profit?
- anonymousLv 74 weeks agoFavorite Answer
The profit function has its maximum when the first derivative equals zero. (The profit function is a quadratic function with a negative leading coefficient, so the graph of it is a downwards-opening parabola and there is one critical point, a maximum.)
P(s) = -25s² + 1300s - 11560
Taking the first derivative, setting that equal to zero, and solving for s gives
-50s + 1300 = 0
s = -1300 / -50
s = 26
= -25(26)² + 1300(26) - 11560
Graph of profit function: