Sure, let's start by analyzing the given functions one by one and then calculating the profit.
We are given the following:
1. Number of video games sold: [tex]\( x = 20 \)[/tex]
2. Revenue function: [tex]\( R(x) = 60x \)[/tex]
3. Cost function: [tex]\( C(x) = 12 + 7x \)[/tex]
4. Profit function: [tex]\( P(x) = 53x - 12^2 \)[/tex]
First, let's compute the revenue [tex]\( R(x) \)[/tex]:
[tex]\[ R(x) = 60x \][/tex]
Substituting [tex]\( x = 20 \)[/tex]:
[tex]\[ R(20) = 60 \times 20 = 1200 \][/tex]
So the revenue from selling 20 video games is \[tex]$1200.
Next, let's compute the cost \( C(x) \):
\[ C(x) = 12 + 7x \]
Substituting \( x = 20 \):
\[ C(20) = 12 + 7 \times 20 = 12 + 140 = 152 \]
So the cost of selling 20 video games is \$[/tex]152.
Finally, let's calculate the profit [tex]\( P(x) \)[/tex]:
[tex]\[ P(x) = 53x - 12^2 \][/tex]
Substituting [tex]\( x = 20 \)[/tex]:
[tex]\[ P(20) = 53 \times 20 - 12^2 \][/tex]
[tex]\[ = 53 \times 20 - 144 \][/tex]
[tex]\[ = 1060 - 144 \][/tex]
[tex]\[ = 916 \][/tex]
Therefore, the profit earned from selling 20 video games is \$916.
