Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Suppose that a tea company estimates that its monthly cost is [tex]$C(x)=500 x^2+100 x$[/tex] and its monthly revenue is [tex]$R(x)=-0.6 x^3+700 x^2-400 x+300$[/tex], where [tex][tex]$x$[/tex][/tex] is in thousands of boxes of tea sold. The profit is the difference between the revenue and the cost.

What is the profit function, [tex]$P(x)$[/tex]?

A. [tex]$P(x)=0.6 x^3-200 x^2+500 x-300$[/tex]

B. [tex][tex]$P(x)=-0.6 x^3+200 x^2-500 x+300$[/tex][/tex]

C. [tex]$P(x)=0.6 x^3+200 x^2-500 x+300$[/tex]

D. [tex]$P(x)=-0.6 x^3+1200 x^2-300 x+300$[/tex]

Sagot :

GinnyAnswer
To find the profit function [tex]\( P(x) \)[/tex], we need to subtract the cost function [tex]\( C(x) \)[/tex] from the revenue function [tex]\( R(x) \)[/tex].

Given the functions:
[tex]\[ C(x) = 500x^2 + 100x \][/tex]
[tex]\[ R(x) = -0.6x^3 + 700x^2 - 400x + 300 \][/tex]

The profit function [tex]\( P(x) \)[/tex] is determined as follows:
[tex]\[ P(x) = R(x) - C(x) \][/tex]

Substitute [tex]\( R(x) \)[/tex] and [tex]\( C(x) \)[/tex] into the equation:
[tex]\[ P(x) = (-0.6x^3 + 700x^2 - 400x + 300) - (500x^2 + 100x) \][/tex]

Now, distribute the negative sign across the terms in [tex]\( C(x) \)[/tex]:
[tex]\[ P(x) = -0.6x^3 + 700x^2 - 400x + 300 - 500x^2 - 100x \][/tex]

Combine like terms:
[tex]\[ P(x) = -0.6x^3 + (700x^2 - 500x^2) + (-400x - 100x) + 300 \][/tex]
[tex]\[ P(x) = -0.6x^3 + 200x^2 - 500x + 300 \][/tex]

Thus, the profit function is:
[tex]\[ P(x) = -0.6x^3 + 200x^2 - 500x + 300 \][/tex]

The correct choice is:
[tex]\[ \boxed{B. \, P(x) = -0.6x^3 + 200x^2 - 500x + 300} \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.