math

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a liquid form of penicillin is sold in bulk at a price of $ 200 per unit.If the total cost for x unit is C(x)=500000+80x+0.003X^2 and the production capacity is at most 30000 at a specified timed, how many of the penicillin must be manufactured and sold in that time to maximize profit?

  • math -

    profit = selling price - cost of making it
    =200x - 500000 - 80x - .0003x^2
    d(profit) = 120 - .006x
    = 0 for a max of profit
    x = 120/.006 = appr. 120

    check:
    at x = 119 , profit = clearly negative
    this question makes no sense to me
    What is that huge number in C(x) supposed to represent?

  • my type error - math -

    x = 120/.006 = 20000

    check:
    let x = 19000, profit = 697000
    let x = 20000, profit = 700000
    let x = 21000, profit = 697000

    the maximum number they should manufacture is
    20000

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