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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]

Sagot :

GinnyAnsweridn
To determine the profit function [tex]\( P(x) \)[/tex], we need to subtract the cost function [tex]\( C(x) \)[/tex] from the revenue function [tex]\( R(x) \)[/tex]. Here are the given functions:

1. Revenue function: [tex]\( R(x) = 60x \)[/tex]
2. Cost function: [tex]\( C(x) = 12 + 7x \)[/tex]

The profit function [tex]\( P(x) \)[/tex] is defined as the difference between the revenue function and the cost function:

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

Let's perform the calculation step-by-step:

1. Write down the revenue function:
[tex]\[ R(x) = 60x \][/tex]

2. Write down the cost function:
[tex]\[ C(x) = 12 + 7x \][/tex]

3. Substitute [tex]\( R(x) \)[/tex] and [tex]\( C(x) \)[/tex] into the profit function formula:
[tex]\[ P(x) = 60x - (12 + 7x) \][/tex]

4. Distribute the negative sign through the parentheses:
[tex]\[ P(x) = 60x - 12 - 7x \][/tex]

5. Combine like terms:
[tex]\[ P(x) = (60x - 7x) - 12 \][/tex]
[tex]\[ P(x) = 53x - 12 \][/tex]

So, the profit function [tex]\( P(x) \)[/tex] is:

[tex]\[ P(x) = 53x - 12 \][/tex]
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