Exercise 2 | Wiskunde op Tilburg University

Antwoord 1 correct

Correct

Antwoord 2 optie

$z(\frac{2}{3},0)=1\frac{4}{9}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$z(0,0)=1$

Antwoord 3 correct

Fout

Antwoord 4 optie

$z(\frac{29}{45},\frac{1}{15})=1\frac{868}{2025}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$z(\frac{9}{14},\frac{1}{14})=1\frac{3}{7}$

Antwoord 1 feedback

Correct:

$3x+y=2$ gives

$y(x)=2-3x$ . We plug this into the object function:

$Z(x)=x^2+3(2-3x)^2+1=28x^2-36x+13$ .

$Z'(x)=56x-36$ and hence,

$x=\frac{9}{14}$ is the only stationary point.

$Z''(x)=56$ , hence

$Z''(\frac{9}{14})=56>0$ . This means we have a minimum.

$y=2-3\cdot \frac{9}{14}=\frac{1}{14}$ . Then

$z(\frac{9}{14},\frac{1}{14})=1\frac{3}{7}$ is a minimum.

Go on.

Antwoord 2 feedback

Wrong: There is an interior solution.

Try again.

Antwoord 3 feedback

Wrong:

$x=0$ and

$y=0$ do not satisfy the constraint

Antwoord 4 feedback

Wrong: Do not just guess.

Try (again).