Question

Maximise ,Z=x+y, subject to $x-y\le -1$, $-x+y\le 0$$x,y\le 0$

Answer 1

$\begin{array}{c}Maximize\\ z=\left(x+y\right)\\ \Rightarrow x-y\le -1,y-x\le 0,x,y\le 0\\ \Rightarrow putx=0inx-y=-1\to \left(i\right)\\ y=1\\ \Rightarrow putx=1inequation\left(i\right)\\ y=2\\ x=-1\\ -1-y=-1\\ y=0\\ andiny-x=0\\ \Rightarrow putx=0\\ y=0\\ \Rightarrow putx=1\\ y=1\\ \Rightarrow putx=2\\ y=2\\ Putx=-1\\ y=-1\end{array}$

No feasible region, hence, no maximum value