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The revenue from selling [tex]x[/tex] shirts is [tex]r(x) = 15x[/tex].

The cost of buying [tex]x[/tex] shirts is [tex]c(x) = 7x + 20[/tex].

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

What is [tex]p(x)[/tex]?

A. [tex]p(x) = 22x - 20[/tex]
B. [tex]p(x) = 8x - 20[/tex]
C. [tex]p(x) = 8x + 20[/tex]
D. [tex]p(x) = 22x + 20[/tex]

Sagot :

GinnyAnsweridn
To determine the profit function [tex]\( p(x) \)[/tex], we need to use the given revenue function [tex]\( r(x) \)[/tex] and cost function [tex]\( c(x) \)[/tex]. The profit function [tex]\( p(x) \)[/tex] is defined as the revenue function minus the cost function:

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

Given:
- The revenue function is [tex]\( r(x) = 15x \)[/tex]
- The cost function is [tex]\( c(x) = 7x + 20 \)[/tex]

Let's substitute these functions into the profit equation:

[tex]\[ p(x) = r(x) - c(x) \][/tex]
[tex]\[ p(x) = 15x - (7x + 20) \][/tex]

Now, we need to simplify the expression inside the parentheses:

[tex]\[ p(x) = 15x - 7x - 20 \][/tex]

Next, combine like terms:

[tex]\[ p(x) = 8x - 20 \][/tex]

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

[tex]\[ p(x) = 8x - 20 \][/tex]

So, the correct answer is:

B. [tex]\( p(x) = 8x - 20 \)[/tex]
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