Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Suppose a granola bar company estimates that its monthly cost is [tex]C(x) = 500x^2 + 400x[/tex] and its monthly revenue is [tex]R(x) = -0.6x^3 + 800x^2 - 300x + 600[/tex], where [tex]x[/tex] is in thousands of granola bars 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) = 0.6x^3 - 300x^2 + 700x - 600[/tex]
B. [tex]P(x) = -0.6x^3 + 300x^2 - 700x + 600[/tex]
C. [tex]P(x) = -0.6x^3 + 1300x^2 + 100x + 600[/tex]
D. [tex]P(x) = 0.6x^3 + 300x^2 - 700x + 600[/tex]

Sagot :

GinnyAnswer
To determine 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 cost function and revenue function:

[tex]\[ C(x) = 500x^2 + 400x \][/tex]
[tex]\[ R(x) = -0.6x^3 + 800x^2 - 300x + 600 \][/tex]

The profit function [tex]\( P(x) \)[/tex] is defined as:

[tex]\[ P(x) = R(x) - C(x) \][/tex]

Substitute the given functions into the equation:

[tex]\[ P(x) = (-0.6x^3 + 800x^2 - 300x + 600) - (500x^2 + 400x) \][/tex]

Now, distribute the negative sign and combine like terms:

[tex]\[ P(x) = -0.6x^3 + 800x^2 - 300x + 600 - 500x^2 - 400x \][/tex]

Combine the [tex]\( x^2 \)[/tex] and [tex]\( x \)[/tex] terms:

[tex]\[ P(x) = -0.6x^3 + (800x^2 - 500x^2) + (-300x - 400x) + 600 \][/tex]

Simplify further:

[tex]\[ P(x) = -0.6x^3 + 300x^2 - 700x + 600 \][/tex]

So, the correct profit function is:

[tex]\[ P(x) = -0.6x^3 + 300x^2 - 700x + 600 \][/tex]

Hence, the correct answer is:

B. [tex]\( P(x) = -0.6x^3 + 300x^2 - 700x + 600 \)[/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.