
Optimization Problem
Hello everyone, I'm so very glad to have found this forum. I'm taking an applied calculus class through correspondence and have been having some difficulties. This is the last class before I can finally graduate, so your help is greatly appreciated!
The problem is a 3 part one, of which I've been able to work through the first two, but am stuck on part 3.
Given:
Basically a restaurant charges $9 for a dish, which results in a demand of 48 orders per night. When the price is raised to $12, there are 42 orders.
Problems:
A)Assume demand is linear and find an equation, which I did. q=2p+66
B)What price should the restaurant charge to maximize its revenue? Again, no problem. $16.50
C) Suppose each dish costs $4 to prepare.
This is where I'm having problems. I believe I'm supposed to come up with a profit function (revenuecost) and find the derivative of that. But if I won't know what my cost will be, how do I do this?
I've been looking over this for a while, so I'm probably missing something simple. I've been putting this class off for over 6 years, so my math skills are very rusty.
Many thanks! I'm sure I will become a regular poster here over the next few weeks as I work hard to finish this course on time.

Re: Optimization Problem
the Revenue (R) from the B) is $\displaystyle R=pq$
similarly, if the profit is P and the cost is c,
$\displaystyle P=(pc)q$
you'll get another quadric equation like in B), find the maxima.

Re: Optimization Problem
Thank you so very much for your help BAdhi! With your help I was able to find the answer to be 18.5.
Best wishes