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The revenue function of a company that sells gaming consoles is [tex]R(x)=6x^2 + 100x + 300[/tex]. The cost function is [tex]C(x) = 25x + 100[/tex]. Which function describes the profit function of the company?

A. [tex]P(x) = 6x^2 + 75x + 200[/tex]

B. [tex]P(x) = 100x^2 - 6x^2[/tex]

C. [tex]P(x) = 75x^2 - 6x^2[/tex]

D. [tex]P(x) = 6x^2 + 200[/tex]

Sagot :

GinnyAnswer
To find the profit function [tex]\( P(x) \)[/tex] of the company, we need to subtract the cost function [tex]\( C(x) \)[/tex] from the revenue function [tex]\( R(x) \)[/tex].

Given revenue function:
[tex]\[ R(x) = 6x^2 + 100x + 300 \][/tex]

Given cost function:
[tex]\[ C(x) = 25x + 100 \][/tex]

The profit function [tex]\( P(x) \)[/tex] is calculated as follows:
[tex]\[ P(x) = R(x) - C(x) \][/tex]

Substitute the given functions into the equation:
[tex]\[ P(x) = (6x^2 + 100x + 300) - (25x + 100) \][/tex]

Now, we simplify the expression:
1. Distribute the negative sign through the cost function:
[tex]\[ P(x) = 6x^2 + 100x + 300 - 25x - 100 \][/tex]

2. Combine like terms:
[tex]\[ P(x) = 6x^2 + (100x - 25x) + (300 - 100) \][/tex]
[tex]\[ P(x) = 6x^2 + 75x + 200 \][/tex]

Therefore, the profit function [tex]\( P(x) \)[/tex] is:
[tex]\[ P(x) = 6x^2 + 75x + 200 \][/tex]

The correct answer is:
A. [tex]\( P(x) = 6x^2 + 75x + 200 \)[/tex]
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