Exercise 1 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: The maximum profit is never negative.

See Example.

Antwoord 3 feedback

Wrong: This producer can make a positive profit.

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.