Example: Consider the CPM project network below, where time is measured in days:
Set up the linear program to determine the critical path.
Solution: Suppose the times are t_0, \dots, t_6 for node 0 to 6. The linear programming is as follows.
| Minimize: | t_6 |
| Subject to: | t_1 - t_0 \ge 6 |
| t_2 - t_0 \ge 5 | |
| t_3 - t_1 \ge 6 | |
| t_3 - t_2 \ge 4 | |
| t_4 - t_1 \ge 8 | |
| t_5 - t_2 \ge 7 | |
| t_5 - t_3 \ge 5 | |
| t_6 - t_2 \ge 2 | |
| t_6 - t_3 \ge 6 | |
| t_6 - t_5 \ge 2 | |
| t_0, t_1, \dots, t_6 \ge 0 |