To determine the company's profit when each sign is sold for [tex]$20, we need to evaluate the given profit function \( p(x) = -10x^2 + 498x - 1500 \) at \( x = 20 \).
Here is the step-by-step solution:
1. Substitute \( x \) with \( 20 \) in the profit function:
\[
p(20) = -10(20)^2 + 498(20) - 1500
\]
2. Calculate \( (20)^2 \):
\[
(20)^2 = 400
\]
3. Now multiply this result by \(-10\):
\[
-10 \times 400 = -4000
\]
4. Next, multiply 498 by 20:
\[
498 \times 20 = 9960
\]
5. Now, sum up the results of these calculations and subtract 1500:
\[
p(20) = -4000 + 9960 - 1500
\]
6. Combine the terms:
\[
-4000 + 9960 = 5960
\]
7. Finally, subtract 1500:
\[
5960 - 1500 = 4460
\]
Therefore, the company's profit if it sells each sign for $[/tex]20 is [tex]$\$[/tex] 4,460[tex]$.
The correct answer is:
C. \$[/tex] 4,460
