To solve this, we need to determine several values step by step based on given formulas.
1. Revenue Calculation:
The revenue function [tex]\( R(x) \)[/tex] is given by:
[tex]\[
R(x) = 60x
\][/tex]
For [tex]\( x = 20 \)[/tex] video games:
[tex]\[
R(20) = 60 \times 20 = 1200
\][/tex]
2. Cost Calculation:
The cost function [tex]\( C(x) \)[/tex] is given by:
[tex]\[
C(x) = 12 + 7x
\][/tex]
For [tex]\( x = 20 \)[/tex] video games:
[tex]\[
C(20) = 12 + 7 \times 20 = 12 + 140 = 152
\][/tex]
3. Profit Calculation:
The profit function [tex]\( P(x) \)[/tex] is the difference between the revenue and the cost:
[tex]\[
P(x) = R(x) - C(x)
\][/tex]
Substituting the values we found:
[tex]\[
P(20) = R(20) - C(20) = 1200 - 152 = 1048
\][/tex]
So, the profit earned from selling 20 video games is:
[tex]\[
P(20) = 1048
\][/tex]
