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Applied Maxima and Minima Problem

  1. Mar 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Problem goes like this:
    For a monopolist's product, the demand equation is: p=156-2q
    and the average-cost is c(ave)=120+112/q

    2. Relevant equations
    We need to find the total cost function in terms of c=

    3. The attempt at a solution

    I can't seem to figure out how to change the average cost of cost....or maybe it's simple and I'm completely missing it....any help would be greatly appreciated!!!!!!
  2. jcsd
  3. Mar 27, 2007 #2


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    Science Advisor

    I'm going to assume that p is the "demand"- the number of items purchased- at price c. (In the future it would be helpful to say things like that explicetely.) Then the revenue is pq= (156-2q)q= 156q- 2q2. The average cost of each item 120- 112/q so the cost of q items is (120- 112/q)q= 120q- 112. (I have no idea what "average cost of cost" means!).

    Finally, the net profit is the revenue minus the cost: 156q- 2q2- (120 q- 112)= 112+ 36q- 2q2. You should be able to find the maximum value of that by completing the square.
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