# The dual of transporting problem

So basically I'm trying to figure out what does a certain variable in dual of transporting problem mean.

Transporting problem in matrix form:

(We are searching for a min cost of transferring goods from node to node across the connections)

\begin{array}{ll} \text{min:} & \ c^Tx \\ \text{} & \ Ax = b \\ & \ x >= 0 \\ \end{array}

\begin{array}{ll} \text{$b_i$ … demand in node i}\\ \text{$c_j$ … cost of transferring one unit of good across the connection j}\\ \text{$x_j$ … number of goods, that we actually transfer across the connection j}\\ & \ \\ \end{array}

Dual:

(We are searching for max amount that the transporter earns by buying all of the goods and then reselling them in nodes)

\begin{array}{ll} \text{max:} & \ b^Ty \\ \text{} & \ A^Ty = c \\ & \ y >= 0 \\ \end{array}

\begin{array}{ll} \text{$b_i$ … ???}\\ \text{$c_j$ … ???}\\ \text{$y_j$ … ???}\\ & \ \\ \end{array}

• I woude like to understand what do variables $b_i$, $c_j$ and $y_j$ mean – Matthew Apr 19 '15 at 21:54