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Video games sold: [tex]\( x \)[/tex]

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

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

Profit function: [tex]\( P(x) = R(x) - C(x) \)[/tex]

What is the profit earned from selling 20 video games?

Sagot :

GinnyAnsweridn
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]
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