Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

The total profit made by an engineering firm is given by the function p=x^2 - 24x +5000 where x is the number of clients the firm has and p is the profit.


1. Find the maximum profit made by the company.

2. How many clients are necessary to reach the profit outlined in part one?

Sagot :

boffeemadrid

Answer:

[tex]5144[/tex]

[tex]12[/tex]

Step-by-step explanation:

The function [tex]p=x^2-24x+5000[/tex] is incorrect as its roots are imaginary [tex]b^2-4ac=576-4\times 5000=-19424<0[/tex].

So, the correct function is

[tex]p=-x^2+24x+5000[/tex]

Differentiating with respect to [tex]x[/tex] we get

[tex]p'=-2x+24[/tex]

Equating with zero

[tex]0=-2x+24\\\Rightarrow x=\dfrac{24}{2}\\\Rightarrow x=12[/tex]

Double derivative of the function

[tex]p''=-2<0[/tex]

So, the function is maximum at [tex]x=12[/tex]

Maximum profit is

[tex]p=-x^2+24x+5000=-12^2+24\times 12+5000\\\Rightarrow p=5144[/tex]

The maximum profit made by the company is [tex]5144[/tex]

The number of clients required to make the maximum profit is [tex]12[/tex].

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.