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Maximise profit

  1. Apr 10, 2004 #1
    I have been trying to figure this out all day. please help.

    If the cost of one unit is $10, 20 units will be sold. If the cost is $11, 18 units will be sold. a) Find the demand function assuming it is linear.
    b) If the materials for each unit cost $6 what should the selling price be to maximise profit?

    I believe that the demand function is p(x)=-.5x+20 but I cannot figure out how to maximise profit. PLEASE HELP!
  2. jcsd
  3. Apr 10, 2004 #2
    If d(p) is the demand as a function of the price, you know that:

    d(p) = Ap + B

    You need to find A and B. You have two pairs of values for d(p) and p, so use them to find A and B:

    20 = 10A + B
    18 = 11A + B

    The function you posted does not seem correct.

    The cost of all units would be 6*d(p). The return value would be d(p)*p. The profit is the difference:

    f(p) = d(p)*p - 6*d(p)

    Now replace d(p) with the actual function:

    f(p) = (Ap + B)*p - 6*(Ap + B) = Ap2 + Bp - 6Ap - 6B

    Find the derivative of f(p), see where it equals zero, etc etc. :smile:
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