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Revenue Function, Profit Function and Maximum Profit

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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.

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Solution Summary

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

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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