Applied Maxima and Minima Problem

  • #1

Homework Statement


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


Homework Equations


We need to find the total cost function in terms of c=


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!!!!!!
 

Answers and Replies

  • #2
HallsofIvy
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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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