Exercise 1 | Wiskunde op Tilburg University

The solution of the following constrained extremum problem is given by

$z(1,2)=8$ .

Determine the corresponding shadow price.

Antwoord 1 correct

Correct

Antwoord 2 optie

$\lambda=0$

Antwoord 2 correct

Fout

Antwoord 3 optie

$\lambda=1\frac{1}{2}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$\lambda=8$

Antwoord 4 correct

Fout

Antwoord 1 optie

$\lambda=2$

Antwoord 1 feedback

Correct:

$L(x,y,\lambda)=xy^3-\lambda(2x^2+\frac{3}{2}y^2-8).$

$L'_x(x,y,\lambda)=y^3-4\lambda x$ . We put these equal to zero and plug in

$(x,y)=(1,2)$ :

$2^3-4\lambda 1=0$ . Rewriting gives

$\lambda=2$ .

Go on.

Antwoord 2 feedback

Wrong: Use the fact that

$z(1,2)=8$ is the maximum.

Try again.

Antwoord 3 feedback

Wrong:

$2^3\neq 6$ .

Try again.

Antwoord 4 feedback

Wrong: The shadow price is not equal to the maximum (value).

See Extra explanation: Schadow price.