To determine the company's profit if it sells each sign for \[tex]$20, we need to substitute \( x = 20 \) into the given profit function \( p(x) = -10x^2 + 498x - 1500 \).
Given:
\[
p(x) = -10x^2 + 498x - 1500
\]
We need to find \( p(20) \).
Step-by-step solution:
1. Substitute \( x = 20 \) into the profit function:
\[
p(20) = -10(20)^2 + 498(20) - 1500
\]
2. Compute each term:
- First term:
\[
-10(20)^2 = -10 \cdot 400 = -4000
\]
- Second term:
\[
498(20) = 9960
\]
- Third term (constant):
\[
-1500
\]
3. Combine the results:
\[
p(20) = -4000 + 9960 - 1500
\]
4. Calculate the final result:
\[
-4000 + 9960 = 5960
\]
\[
5960 - 1500 = 4460
\]
Therefore, the company's profit when each sign is sold for \$[/tex]20 is \[tex]$4460.
The correct answer is:
C. \(\$[/tex]4,460\)
