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I have a problem where my answer does not seem to be right anywhere. For the following set up:

Budget constraint: $400=40x+20y$

Utility function: $u(x,y)=3x+y$

the problems asks to derive the demand function for $x$ (for the given $p_y$). And I get to:

$$x=f(p_x)= \begin{cases} \frac{400}{p_x}\quad\quad &if\quad p_x<60\\ 0\quad\quad &if\quad p_x>60\\ \left(0,\frac{400}{p_x}\right)\quad\quad &if\quad p_x=60 \end{cases} $$

When I graph this, I get the following chart: enter image description here

I was told that the step between 40 and 60 for $p_x$ should not be there, but I can not figure out why. Can someone please explain what am I missing?

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    $\begingroup$ 1. Your description $$x=f(p_x)= \begin{cases} \frac{400}{p_x}\quad\quad &if\quad p_x<60\\ 0\quad\quad &if\quad p_x>60\\ \left(0,\frac{400}{p_x}\right)\quad\quad &if\quad p_x=60 \end{cases} $$ has only three segments. How come your graph has four? $\endgroup$
    – Giskard
    May 28, 2021 at 5:26
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    $\begingroup$ 2. $\frac{400}{60}$ is not close to 10, but close to 7, so demand at $p_x =60$ should not stretch from 0 to ten-ish. $\endgroup$
    – Giskard
    May 28, 2021 at 5:27

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