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Video games sold: [tex]$x$[/tex]

Revenue function: [tex]$R(x) = 60x$[/tex]

Cost function: [tex][tex]$C(x) = 12 + 7x$[/tex][/tex]

Profit function: [tex]$P(x) = 53x - 12^2$[/tex]

What is the profit earned from selling 20 video games?

Sagot :

GinnyAnsweridn
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.
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