ECE Ph.D. Qualifying Exam: Automatic Control (AC)- Question 3, August 2011
$ \color{blue}\text{3. } \left( \text{20 pts} \right) \text{ Solve the following linear program, } $
maximize − x1 − 3x2 + 4x3
subject to $ x_{1}+2x_{2}-x_{3}=5 $
$ 2x_{1}+3x_{2}-x_{3}=6 $
$ x_{1} \text{ free, } x_{2}\geq0, x_{3}\leq0. $
$ \color{blue}\text{Solution 1:} $
$ \Rightarrow x_{1}=5-2x_{2}+x_{3}=3-\frac{3}{2}x_{2}+\frac{1}{2}x_{3} $
$ \Rightarrow x_{2}-x_{3}=4 $
