IDNLearn.com provides a collaborative environment for finding and sharing answers. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
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]
[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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.