Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

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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  • 4 weeks ago
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    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:

    https://www.desmos.com/calculator/40vj1dpq7o

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