Exercise 1 | Wiskunde op Tilburg University

Antwoord 1 correct

Correct

Antwoord 2 optie

$U(\frac{2}{3},10\frac{2}{3})=2\frac{2}{3}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$U(1\frac{1}{3},5\frac{1}{3})=2\frac{2}{3}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$U(4,4)=4$

Antwoord 4 correct

Fout

Antwoord 1 optie

$U(1,8)=\sqrt{8}$

Antwoord 1 feedback

Correct:

$\dfrac{U'_x(x,y)}{U'_y(x,y)}=\dfrac{\frac{1}{2}x^{-\frac{1}{2}}y^{\frac{1}{2}}}{\frac{1}{2}x^{\frac{1}{2}}y^{-\frac{1}{2}}}=\dfrac{8}{1}$ gives

$8x=y$ . We plug this into the restriction:

$8x+8x=16$ . Hence,

$x=1$ and that gives

$y=8$ .

$U(1,8)=\sqrt{8}$ . We determine via the boundary points whether this is a maximum.

$U(2,0)=0$ and

$U(0,16)=0$ and hence

$U(1,8)=\sqrt{8}$ is the maximum.

Go on.

Antwoord 2 feedback

Wrong:

$\dfrac{U'_x(x,y)}{U'_y(x,y)}=\dfrac{\frac{1}{2}x^{-\frac{1}{2}}y^{\frac{1}{2}}}{\frac{1}{2}x^{\frac{1}{2}}y^{-\frac{1}{2}}}$ .

Try again.

Antwoord 3 feedback

Wrong:

$\dfrac{U'_x(x,y)}{U'_y(x,y)}=\dfrac{\frac{1}{2}x^{-\frac{1}{2}}y^{\frac{1}{2}}}{\frac{1}{2}x^{\frac{1}{2}}y^{-\frac{1}{2}}}$ .

Try again.

Antwoord 4 feedback

Wrong:

$(x,y)=(4,4)$ is not allowed, because

$8\cdot 4+4\neq 16$ .

Try again.