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Math Help - need help for this question! ASAP, Thanks

  1. #1
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    need help for this question! ASAP, Thanks

    A marketing researcher has determined that when a product sells at x dollars per unit' the number of units sold per week is given by the function
    q= 75/x-m + 80(5m -x)
    where m > 0 is the total manufactunng cost in dollar per unit and m < x <5m.
    (a) Find the profit function P(x) (in dollars per week) and simplify it.
    (b) Use calculus to find the selling price x that maximizes weekly profit. Sufficiently justify your solution
    (c) Use your answer to part (b) to determine the manufacturing cost m that yields a maximum weekly profit of 3,455 dollar

    thanks
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  2. #2
    Junior Member
    Joined
    Feb 2009
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    p(x) = (x-m)q
    substitute to get your function

    p(x) = 75+80(5m-x)(x-m)

    dp/dx = 80(6m-2x)

    to maximize equate to zero

    80(6m-2x) = 0

    x = 3m

    3455 = 75 + 80(2m)(2m)

    m = 3.25
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