Exercise 4 | Wiskunde op Tilburg University

Which of the following graphs depicts the level curves of

$z(x,y)=\min\{2x,5y\}$ with values

$k=5$ and

$k=10$ ?

Antwoord 1 correct

Correct

Antwoord 2 optie

Antwoord 2 correct

Fout

Antwoord 3 optie

Antwoord 3 correct

Fout

Antwoord 4 optie

Antwoord 4 correct

Fout

Antwoord 1 optie

Antwoord 1 feedback

Correct: The rewriting of

$\min\{2x,5y\} = k$ for

$k=5$ gives:

$\left\{\begin{array}{ll} 2x = 5 &\text{if~}5y\geq5\\ 5y= 5 &\text{if~}2x\geq5 \end{array}\right. \iff \left\{\begin{array}{ll} x = 2\tfrac{1}{2} &\text{if~}y\geq1\\ y= 1 &\text{if~}x\geq2\tfrac{1}{2} \end{array}\right.$
The corresponding graph is the left curve. The rewriting of

$\min\{2x,5y\} = k$ for

$k=10$ gives:

$\left\{\begin{array}{ll} 2x = 10 &\text{if~}5y\geq10\\ 5y= 10 &\text{if~}2x\geq10 \end{array}\right. \iff \left\{\begin{array}{ll} x = 5 &\text{if~}y\geq2\\ y= 2 &\text{if~}x\geq5 \end{array}\right.$
The corresponding graph is the right curve.

Go on.

Antwoord 2 feedback

Wrong: Pay attention to the rewriting of

$z(x,y)=k$ : you probably interchanged

$x$ and

$y$ .

See Example 1, Example 2 and in particular Example 3.

Antwoord 3 feedback

Wrong: Pay attention to the rewriting of

$z(x,y)=k$ : you probably forgot the restrictions.

See Example 1, Example 2 and in particular Example 3.

Antwoord 4 feedback

Wrong: The

$2$ of

$2x$ and the

$5$ of

$5y$ do not provide the coordinates of the corner point of the curve.

See Example 1, Example 2 and in particular Example 3.