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

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

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

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



Answer :

GinnyAnswer
To determine the profit function \( p(x) \) from selling \( x \) shirts, we need to subtract the cost function from the revenue function.

Given:
- Revenue function \( r(x) = 15x \)
- Cost function \( c(x) = 7x + 20 \)
- Profit function \( p(x) = r(x) - c(x) \)

We start by writing the profit function in terms of \( r(x) \) and \( c(x) \):
[tex]\[ p(x) = r(x) - c(x) \][/tex]

Substitute the given functions into the equation:
[tex]\[ p(x) = 15x - (7x + 20) \][/tex]

Next, distribute the subtraction inside the parentheses:
[tex]\[ p(x) = 15x - 7x - 20 \][/tex]

Combine like terms:
[tex]\[ p(x) = (15x - 7x) - 20 \][/tex]
[tex]\[ p(x) = 8x - 20 \][/tex]

Therefore, the correct expression for the profit function \( p(x) \) is:
[tex]\[ p(x) = 8x - 20 \][/tex]

Hence, the correct answer is:
B. [tex]\( p(x)=8 x-20 \)[/tex]

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