2004-43.md

course	course_year	question_number	tags	title	year
Optimization	IB	43	IB 2004 Optimization	3.II.23G	2004

Consider the following linear programming problem:

$$\begin{aligned} \text { maximize }-x_{1}+3 x_{2} \\ \text { subject to } \quad x_{1}+x_{2} & \geqslant 3 \\ -x_{1}+2 x_{2} & \geqslant 6 \\ -x_{1}+x_{2} & \leqslant 2, \\ x_{2} & \leqslant 5, \\ x_{i} & \geqslant 0, \quad i=1,2 . \end{aligned}$$

Write down the Phase One problem in this case, and solve it.

By using the solution of the Phase One problem as an initial basic feasible solution for the Phase Two simplex algorithm, solve the above maximization problem. That is, find the optimal tableau and read the optimal solution $\left(x_{1}, x_{2}\right)$ and optimal value from it.