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]
