\(maximize \hskip 1.1cmx_1+2x_2-\hskip2.8mmx_3\)
\(subject\hskip2mmto:\hskip5mm2x_1+2x_2-2x_3\hskip 3mm \le\hskip 3mm 10\)
\(3x_1-2x_2+2x_3\hskip 3mm \le\hskip 3mm 5\)
\(x_1-4x_2+\hskip 2.8mmx_3\hskip 3mm \le\hskip 3mm 10\)
\(x_1,x_2,x_3\hskip 3mm\ge\hskip 3mm0\)
+33659 On looking at this further it seems that there is no unique answer;
Choose x1 = 3; any value for x2 (>2); x3 = x2 - 2, and you get:
2x1 + 2x2 - 2x3 = 10
3x1 - 2x2 + 2x3 = 5
x1 - 4x2 + x3 = 1 - 3x2 (<10)
with x1 + 2x2 - x3 = 5 + x2
These satisfy all the conditions with the target being 5 more than the value chosen for x2
