To find the profit earned from selling 20 video games, let's go through the problem step-by-step.
1. Determine the Revenue Function [tex]\( R(x) \)[/tex]:
The revenue function is given by [tex]\( R(x) = 60x \)[/tex]. Here, `x` represents the number of video games sold.
Since we need to find the revenue from selling 20 video games, substitute [tex]\( x = 20 \)[/tex] into the revenue function:
[tex]\[
R(20) = 60 \times 20 = 1200
\][/tex]
2. Determine the Cost Function [tex]\( C(x) \)[/tex]:
The cost function is given by [tex]\( C(x) = 12 + 7x \)[/tex].
Substitute [tex]\( x = 20 \)[/tex] into the cost function to find the total cost for 20 video games:
[tex]\[
C(20) = 12 + 7 \times 20 = 12 + 140 = 152
\][/tex]
3. Determine the Profit Function [tex]\( P(x) \)[/tex]:
The profit function is defined as the revenue minus the cost, [tex]\( P(x) = R(x) - C(x) \)[/tex].
Substitute [tex]\( R(20) \)[/tex] and [tex]\( C(20) \)[/tex] into the profit function to find the profit:
[tex]\[
P(20) = R(20) - C(20) = 1200 - 152 = 1048
\][/tex]
Therefore, the profit earned from selling 20 video games is [tex]\( 1048 \)[/tex].
