**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 |