(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose you are given the following inequality

[tex]-6x+ 4y+ 10z \leq 1203[/tex]

[tex]7y + 15z \leq 1551[/tex]

[tex]x,y,z \geq 0[/tex]

Find a K > 0, if it exists, such that [tex]|x| \leq K[/tex], [tex]|y| \leq K[/tex], [tex]|z| \leq K[/tex]

Flyingpig's take on this

So I am just going find the max of each x,y,z

Let x = 0, y = 0

[tex]10z \leq 1203 \iff z \leq 120.3[/tex]

[tex] 15z \leq 1551 \iff z \leq 103.4[/tex]

So it makes sense to take [tex]z \leq 103.4[/tex] and that [tex]|z| \leq 103.4[/tex]

Let x = 0, z = 0

[tex]4y \leq 1203 \iff y \leq 300.75[/tex]

[tex]7y \leq 1551 \iff y \leq 221.57[/tex]

Take [tex]y \leq 221.57[/tex] and that [tex]|y| \leq 221.57[/tex]

Let y = 0, z = 0

[tex]-6x \leq 1203 \iff x \geq -200.5[/tex]

[tex]0 \leq 1551[/tex]

However [tex]x \geq 0[/tex], so [tex]|x| \geq 0[/tex]

Side Question - not part of this thread

Was [tex]0 \leq 1551[/tex] useless? Also I know I am wrong, but I need to someone to give me a formal reason why I couldn't [tex]|x| \leq |-200.5|[/tex] and it becomes that [tex]|x| \leq 200.5[/tex]

Side Question - ended, carry on with calculation below

So we have

[tex]|x| \geq 0[/tex]

[tex]|y| \leq 221.57[/tex]

[tex]|z| \leq 103.4[/tex]

Now what does [tex]|x| \geq 0[/tex] imply? Does it say that any [tex]K \geq 221.57[/tex] will satisfy the inequalities [tex]|x| \leq K[/tex], [tex]|y| \leq K[/tex], [tex]|z| \leq K[/tex]

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# Absolute valuing both sides probably a big no-no in Math

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