# Revenue Function, Profit Function and Maximum Profit

Problem:
A company makes cameras.
The price per camera at which x million cameras can be sold is:
p(x) = 94.8 - 5x.

0 -< x -< 15
(the symbol -< is the "greater or equal to sign", I couldn't get it to work on my computer)

The cost of making x million cameras is:
c(x) = 156 + 19.7x
(x is in millions of \$)

Questions:
1. Write the revenue function r(x).
2. How many cameras must be sold to have a revenue of at least \$400,000,000?
3. Write the profit function p(x).
4. What is the maximum profit to the nearest dollar?
5. How many cameras must be sold to break even?
6. What is the price per camera which maximizes profit?

My question for you:
I am in math 104, finite mathematics. We use graphing calculators for our projects, I have a TI83. The problem is all about functions such as Revenue, Profit, Break Even point, Maximizing profit, and so on. I know that to answer some of the problems, you would have to graph the functions on the graphing calculator somehow, and then do some sort of calculation on the calculator with them, such as "2nd... calculate... maximize" or "2nd... calculate...minimize" etc.
I'm not sure, but for problem number one, my answer for the revenue function is "r(x)= x(94.8 - 5x)" but I am not positive. I have no idea how to do problem number 2,4,5 or 6. Problem number three my answer would be "p(x)= x(94.8 - 5x) - 156 + 19.7x" but again, I'm not sure.
I need help with problems 1 through 6. I need to know how to work the problems, and I need to know the correct answers.

This question has the following supporting file(s):

###### File Viewer (Click To Zoom)

Solution Summary

A revenue function, profit function and the maximum profit calculations are shown. The solution is well presented.

\$2.19
###### This answer includes:
• Plain text
• Cited sources when necessary
• Attached file(s)
• Math 104.doc
Add to Cart   \$2.19

Changping Wang, MA

Rating 4.9/5

Active since 2003

BSc , Wuhan Univ. China
MA, Shandong Univ.

Responses 6078

Comments on Changping's work:

"Thanks for doing this I have another similar questions. If you are interested I can post it to you"

"Thanks! Let me know if you want to help out for a derivation for the same problem but this time only for the integration version?"

"Thank you. Can I please trouble you to show all work for the first problem? (x + 3)(x − 5) < 0"

"Thank you!"

"I would like for you to be my expect. I will save your ID. Thanks a million times."