Linear Programming $\boldsymbol{c}^T \boldsymbol{x}$ s.t. $\boldsymbol{Ax} = \boldsymbol{b}$

Asked Mar 12 '15 at 10:01

Active Mar 12 '15 at 10:01

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Prove for the linear programming \begin{equation} \left\{ \begin{array}{cc} min & \boldsymbol{c}^T \boldsymbol{x} \\ s.t. & \boldsymbol{Ax} = \boldsymbol{b} \end{array} \right. \end{equation} has only two results:

the objective function dose not have lower bound.
all the feasible solutions are optimal.

if the feasible domain is not empty.

asked Mar 12 '15 at 10:01

Huayu Zhang

I'm not sure I quite understand. All feasible solutions will be optimal if the objective function is just a constant right? – Dipole Mar 12 '15 at 10:49
@Jack Yes, the objective function is constant in result 2. – Huayu Zhang Mar 12 '15 at 11:27

Linear Programming $\boldsymbol{c}^T \boldsymbol{x}$ s.t. $\boldsymbol{Ax} = \boldsymbol{b}$

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