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]
