# Finding the most Profitable Price

• Oct 3rd 2011, 04:37 PM
er7
Finding the most Profitable Price
I am given this problem:

A producer finds that demand for his commodity obeys a linear demand equation p+7.5x=80, where p is in dollars and x in thousands of units. If the cost equation is C(x)=6x2+70x+1.25 , what price should be charged to maximize the profit?

Now I've been solving a lot of problems like this lately... I know how to go through the steps and maximize or minimize a function by finding P(x) if it isn't given, taking the derivative, and setting it equal to 0...

However, I've only worked with maximizing profit in relation to the number of items sold so far. I haven't done this with profit yet.

What other pieces of information do I need to calculate to figure this one out?
• Oct 3rd 2011, 06:26 PM
MonroeYoder
Re: Finding the most Profitable Price
Profit = Revenue - Cost

You're given cost so we just have to find revenue. Revenue equals the number of items sold (\$\displaystyle x\$) times the price they sell for (\$\displaystyle p\$). But we know \$\displaystyle p=80-7.5x\$ so our Revenue \$\displaystyle = xp = x(80-7.5x)\$

Now you can find the profit function and go through the whole sha-bang of taking a derivative of profit and setting it equal to zero