Is function $x_1+x_2+x_3+x_4$ bounded on the domain $D:=\{(x_1,x_2,x_3,x_4) | x_1-x_2-3x_3+x_4 = 5, 2x_1+2x_2+x_3-2x_4 = 4,\& \quad \forall i: x_i \geq 0\}$
I have no idea on how to find an answer. Can anyone give me some hints?
Is funtion Is function $x_1+x_2+x_3+x_4$ bounded on$D:=\{(x_1,x_2,x_3,x_4) | x_1-x_2-3x_3+x_4 = 5, 2x_1+2x_2+x_3-2x_4 = 4, x_i \geq 0\}$
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calculus
linear-algebra
optimization
linear-programming
1 Answers
2
No. Let $x_3 = 0$ then, $x_1-x_2 = 5-x_4, x_1+x_2 = x_4+2$. So, $x_1 = 3.5, x_2 = x_4-1.5$ and $x_1+x_2+x_3+x_4 = 2x_4+2 $ is unbounded.