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The revenue from selling [tex]\( x \)[/tex] hats is [tex]\( r(x) = 18x \)[/tex].

The cost of buying [tex]\( x \)[/tex] hats is [tex]\( c(x) = 8x + 30 \)[/tex].

The profit from selling [tex]\( x \)[/tex] hats is [tex]\( p(x) = r(x) - c(x) \)[/tex].

Write a function for [tex]\( p(x) \)[/tex], the profit from selling [tex]\( x \)[/tex] hats.

A. [tex]\( p(x) = 10x + 30 \)[/tex]

B. [tex]\( p(x) = 26x - 30 \)[/tex]

C. [tex]\( p(x) = 10x - 30 \)[/tex]

D. [tex]\( p(x) = 26x + 30 \)[/tex]

Sagot :

GinnyAnsweridn
To determine the profit function [tex]\( p(x) \)[/tex], we need to find the difference between the revenue function [tex]\( r(x) \)[/tex] and the cost function [tex]\( c(x) \)[/tex].

First, let's explicitly write down the given functions:

- The revenue function is [tex]\( r(x) = 18x \)[/tex].
- The cost function is [tex]\( c(x) = 8x + 30 \)[/tex].

The profit function [tex]\( p(x) \)[/tex] is defined as the revenue minus the cost. Therefore, we have:

[tex]\[ p(x) = r(x) - c(x) \][/tex]

Substitute the given functions into the equation:

[tex]\[ p(x) = 18x - (8x + 30) \][/tex]

Next, distribute the negative sign inside the parentheses:

[tex]\[ p(x) = 18x - 8x - 30 \][/tex]

Combine like terms:

[tex]\[ p(x) = (18x - 8x) - 30 \][/tex]

[tex]\[ p(x) = 10x - 30 \][/tex]

Therefore, the profit function [tex]\( p(x) \)[/tex] is:

[tex]\[ p(x) = 10x - 30 \][/tex]

Among the given options, the correct answer is:

C. [tex]\( p(x) = 10x - 30 \)[/tex]
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