Find expert answers and community support for all your questions on IDNLearn.com. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

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]


Sagot :

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]