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# 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?

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- 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

maximum profit

= P(26)

= -25(26)² + 1300(26) - 11560

= 5340

Graph of profit function:

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