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    kebone's Avatar
    kebone Posts: 1, Reputation: 1
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    #1

    Sep 18, 2008, 02:04 AM
    Finding the profit function.
    A firm maximises profitt at 5 units, breakeven at 8 units, but loses 10 000 if nothing is sold, determine the quadratic function relating to units sold.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Sep 19, 2008, 01:38 PM
    Starting with the general form of the quadratic equation:



    what you want to do is determine values for b and c in terms of a, then solve for a.

    From the first condition you know that the derivative of y equals zero at x = 5


    Therefore

    So now you can substitue for b in the basic quadratic equation.

    The second piece of information you were given tells you that the value of y is 0 at x = 8, so:



    From this you can express c in terms of a.

    Finally the last condition tells you that y(0) = -10000. From this you can now determine the value of a.

    Hope this helps.
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