12th Calculus

it cost you c dollars each to manufacture and distribute backpacks. if the backpacks sell at x dollars each, the number sold is given by

n=(a/x-c)+b(100-x)

where a and b are certain positive constanst. what selling price will bring a maximum profit?

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  1. Profit as a function of x is

    P(x) = n (x - c)
    = a - cx + 100 bx - bx^2 - cx

    Maximum profit occurs when dP/dx = 0
    -2c + 100 b = 2xb
    x = -c/b + b/50

    Check my work.

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