Applied Maxima and Minima Problem

[jennifer361]

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!

 

[HallsofIvy]

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.