A Railroad Needs to Move the Maximum Amount of Material

Question

Examlex · Accepted Answer

The Answer is

ext { MAX: } \quad X_{61}

Subject to:

\begin{array}{ll}X_{61}-X_{12}-X_{13}=0 & \\mathrm{X}_{12}-\mathrm{X}_{25}=0 & \\mathrm{X}_{13}-\mathrm{X}_{35}-\mathrm{X}_{34}=0 & \\mathrm{X}_{34}-\mathrm{X}_{46}=0 & \\mathrm{X}_{25}+\mathrm{X}_{35}-\mathrm{X}_{56}=0 & \\mathrm{X}_{56}+\mathrm{X}_{46}-\mathrm{X}_{61}=0 & \0 \leq \mathrm{X}_{12} \leq 5 & 0 \leq \mathrm{X}_{13} \leq 4 \0 \leq \mathrm{X}_{25} \leq 6 & 0 \leq \mathrm{X}_{35} \leq 6 \0 \leq \mathrm{X}_{34} \leq 6 & 0 \leq \mathrm{X}_{56} \leq 8 \0 \leq \mathrm{X}_{46} \leq 2 & 0 \leq \mathrm{X}_{61} \leq \infty\end{array}

Definitions: