Tuesday, May 6, 2014

An simple example of linear programming 2

To simplify,

Minimize

\begin{align*} c_1 x_1 + c_2 x_2 \end{align*}

Under the constraint

\begin{align*} a_{11} x_1 + a_{12} x_2 + x_3 + 0 &= B \\ a_{21} x_1 + a_{22} x_2 + 0 + x_4 &= B \\ \end{align*}

In matrix language:

Minimize \begin{align*} c^T x \end{align*}

where $c = (c_1, c_2, 0, 0)$.

Under constraint

\begin{align*} \begin{pmatrix} A & I_2 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \\ \end{pmatrix} &= B \\ \end{align*}

1 comments:

Unknown said...

Note how an inequality constraint is cleverly turned into a equality constraint.