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Select the correct answer.

A home-based sign company uses this function to model its monthly profit, where [tex][tex]$x$[/tex][/tex] is the price of each sign it sells.
[tex]
p(x) = -10x^2 + 498x - 1,500
[/tex]

What is the company's profit if it sells each sign for [tex]\[tex]$20[/tex]?

A. [tex]\$[/tex]1,402[/tex]

B. [tex]\[tex]$14,420[/tex]

C. [tex]\$[/tex]18,020[/tex]

D. [tex]\$4,460[/tex]



Answer :

GinnyAnswer
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]