- Minimize $z(x,y)=x^2+3y^2+1$
- Subject to $3x+y=2$
- Where $x,y\geq0$
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.
Go on.
Antwoord 2 feedback
Wrong: There is an interior solution.
Try again.
Try again.
Antwoord 3 feedback
Wrong: $x=0$ and $y=0$ do not satisfy the constraint $3x+y=2$.
See Constrained optimizaton functions of two variables.
See Constrained optimizaton functions of two variables.
Antwoord 4 feedback
Wrong: Do not just guess.
Try (again).
Try (again).