please help
The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by
q = (107 − 2p)^2,
where p is the price per dumbbell, and q is the demand in weekly sales. Find the price Professor Schwarzenegger should charge for his dumbbells in order to maximize revenue.

Question

please help
The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by
q = (107 − 2p)^2,
where p is the price per dumbbell, and q is the demand in weekly sales. Find the price Professor Schwarzenegger should charge for his dumbbells in order to maximize revenue.

tkhunny · Answer

Please provide the Revenue Equation.  It's not QUITE given in the problem statement.

anonymous · Answer

It did not give me any other equation.

tkhunny · Answer

I understand that.  Creating it is the thinking part of this problem.

anonymous · Answer

revenue is p*q right?

tkhunny · Answer

That's it.  Substitute for q from the demand equation and you'll have it.

anonymous · Answer

what do I substitute for q?

tkhunny · Answer

Revenue is p*q.  You need to maximize this, finding the price that does so.  As "DEMAND" doesn't do us any good toward this goal, let's get rid of it.

p*q = p*((107 − 2p)^2)

Now, we have R(p), Revenue as a function of Price alone.

Now comes the calculus part.