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\(maximize \hskip 1.1cmx_1+2x_2-\hskip2.8mmx_3\)

 

\(subject\hskip2mmto:\hskip5mm2x_1+2x_2-2x_3\hskip 3mm \le\hskip 3mm 10\)

                            \(3x_1-2x_2+2x_3\hskip 3mm \le\hskip 3mm 5\)

                              \(x_1-4x_2+\hskip 2.8mmx_3\hskip 3mm \le\hskip 3mm 10\)

                                         \(x_1,x_2,x_3\hskip 3mm\ge\hskip 3mm0\)

 Feb 9, 2016
 #1
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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

 Feb 9, 2016
edited by Alan  Feb 9, 2016

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