To solve for Luisa's profit function [tex]\( p(x) \)[/tex], we need to find the difference between her revenue function [tex]\( f(x) \)[/tex] and her cost function [tex]\( d(x) \)[/tex].
Given:
- The revenue function is [tex]\( f(x) = 20x \)[/tex].
- The cost function is [tex]\( d(x) = 4x + 25 \)[/tex].
The profit function [tex]\( p(x) \)[/tex] is defined as the revenue minus the cost:
[tex]\[ p(x) = f(x) - d(x) \][/tex]
Let's find [tex]\( p(x) \)[/tex] step by step:
1. Substitute the revenue function [tex]\( f(x) \)[/tex] and the cost function [tex]\( d(x) \)[/tex] into the profit function:
[tex]\[ p(x) = 20x - (4x + 25) \][/tex]
2. Distribute the negative sign through the cost function:
[tex]\[ p(x) = 20x - 4x - 25 \][/tex]
3. Combine like terms:
[tex]\[ p(x) = 16x - 25 \][/tex]
Therefore, the profit function is:
[tex]\[ p(x) = 16x - 25 \][/tex]
The correct answer is:
B. [tex]\( p(x)=16x-25 \)[/tex]
