Certainly! Let's analyze the given functions step-by-step to determine the Profit function [tex]\( P(x) \)[/tex].
### Step-by-Step Solution
1. Revenue Function: The revenue function represents the total income generated from selling [tex]\( x \)[/tex] video games. Here it is given by:
[tex]\[
R(x) = 60x
\][/tex]
This means for each video game sold, [tex]$60 is earned in revenue.
2. Cost Function: The cost function represents the total cost incurred for producing \( x \) video games. Here it is given by:
\[
C(x) = 12 + 7x
\]
This function indicates that there is a fixed cost of $[/tex]12, plus an additional cost of $7 for each video game produced.
3. Profit Function: The profit function is obtained by subtracting the cost function from the revenue function, i.e.,
[tex]\[
P(x) = R(x) - C(x)
\][/tex]
4. Derive the Profit Function:
[tex]\[
P(x) = 60x - (12 + 7x)
\][/tex]
5. Simplify the Equation:
[tex]\[
P(x) = 60x - 12 - 7x
\][/tex]
Combine like terms:
[tex]\[
P(x) = (60x - 7x) - 12
\][/tex]
[tex]\[
P(x) = 53x - 12
\][/tex]
### Conclusion
The profit function [tex]\( P(x) \)[/tex] for selling [tex]\( x \)[/tex] video games is:
[tex]\[
P(x) = 53x - 12
\][/tex]
So, the Profit function is [tex]\( P(x) = \boxed{53x - 12} \)[/tex].
