A producer is a price-taker and the price of one unit of output is 8. The cost function of the producer is $C(y)=\frac{1}{3}y^3-5\frac{1}{2}y^2+26y$. Determine the maximum profit.
Antwoord 1 correct
Correct
Antwoord 2 optie
$-27\frac{2}{3}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$0$
Antwoord 3 correct
Fout
Antwoord 4 optie
$66\frac{388}{999}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$40\frac{1}{2}$
Antwoord 1 feedback
Correct: It follows that $R(y)=8y$, which implies that $\pi(y)=-\frac{1}{3}y^3+5\frac{1}{2}y^2-18y$.
Hence, $\pi'(y)=-y^2+11y-18=0$, which gives $y=2$ or $y=9$. Using a sign chart we find that $y=9$ is a maximum location. The maximum profit is then $\pi(9)=40\frac{1}{2}$, which is positive.
Go on.
Hence, $\pi'(y)=-y^2+11y-18=0$, which gives $y=2$ or $y=9$. Using a sign chart we find that $y=9$ is a maximum location. The maximum profit is then $\pi(9)=40\frac{1}{2}$, which is positive.
Go on.
Antwoord 2 feedback
Antwoord 3 feedback
Wrong: This producer can make a positive profit.
Try again.
Try again.
Antwoord 4 feedback
Wrong: Consider the minus-signs: $\pi(y)\neq -\frac{1}{3}y^3-5\frac{1}{2}y^2+34y$.
Try again.
Try again.