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3x4 system of inequalities given, max |x|+|y|+|z| (HOMC 2016 J Q9)
3x4 system of inequalities given, max |x|+|y|+|z| (HOMC 2016 J Q9)
Source:
August 7, 2019
inequalities
System
maximum
algebra
Problem Statement
Let
x
,
y
,
z
x, y,z
x
,
y
,
z
satisfy the following inequalities
{
∣
x
+
2
y
−
3
z
∣
≤
6
∣
x
−
2
y
+
3
z
∣
≤
6
∣
x
−
2
y
−
3
z
∣
≤
6
∣
x
+
2
y
+
3
z
∣
≤
6
\begin{cases} | x + 2y - 3z| \le 6 \\ | x - 2y + 3z| \le 6 \\ | x - 2y - 3z| \le 6 \\ | x + 2y + 3z| \le 6 \end{cases}
⎩
⎨
⎧
∣
x
+
2
y
−
3
z
∣
≤
6
∣
x
−
2
y
+
3
z
∣
≤
6
∣
x
−
2
y
−
3
z
∣
≤
6
∣
x
+
2
y
+
3
z
∣
≤
6
Determine the greatest value of
M
=
∣
x
∣
+
∣
y
∣
+
∣
z
∣
M = |x| + |y| + |z|
M
=
∣
x
∣
+
∣
y
∣
+
∣
z
∣
.
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