Math

A chain store manager has been told by the main office that daily profit, P is related to the number of clerks working that day, x, according to the equation P= -25x^2 + 300x. What number of clerks will maximize the profit, and what is the maximum possible profit?

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  1. if you know Calculus ....
    dP/dx = -50x + 300 = 0 for a max of P
    x = 6
    P= -25(36) + 300(6) = 900

    otherwise complete the square ....

    P = -25(x^2 - 12x + 36-36)
    = -25( (x-6)^2 - 36)
    = -25(x-6)^2 + 900

    same as above

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