Let's analyze the profitability of a home-based sign company based on the provided profit function, which is given by the equation:
[tex]\[
p(x) = -10x^2 + 498x - 1500
\][/tex]
Here, [tex]\( x \)[/tex] represents the price per sign in dollars.
To find the company's profit when the price per sign is [tex]$20, we substitute \( x = 20 \) into the profit function:
\[
p(20) = -10(20)^2 + 498(20) - 1500
\]
After performing the calculations:
\[
p(20) = -10 \cdot 400 + 498 \cdot 20 - 1500
\]
\[
p(20) = -4000 + 9960 - 1500
\]
\[
p(20) = 5960 - 1500
\]
\[
p(20) = 4460
\]
Therefore, the company's profit when selling each sign for $[/tex]20 is [tex]\(\$4460\)[/tex].
The correct answer is:
D. [tex]\(\$4460\)[/tex]
