# 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.

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• Math 104.doc
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A revenue function, profit function and the maximum profit calculations are shown. The solution is well presented.

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Changping Wang, MA

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Extracted Content from Question Files:

• Math 104.doc

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.