**Problem:**

You are given the following mode choice model.

Where:

- = travel cost between and by mode
- = dummy variable (alternative specific constant) for transit

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 5 | 7 |

New Fargo | 7 | 5 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 10 | 15 |

New Fargo | 15 | 8 |

**Solution:**

**Part A**

A. Using a logit model, determine the probability of a traveler driving.

Solution Steps

- Compute Utility for Each Mode for Each Cell
- Compute Exponentiated Utilities for Each Cell
- Sum Exponentiated Utilities
- Compute Probability for Each Mode for Each Cell
- Multiply Probability in Each Cell by Number of Trips in Each Cell

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | -5 | -7 |

New Fargo | -7 | -5 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | -5 | -10 |

New Fargo | -10 | -3 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 0.0067 | 0.0009 |

New Fargo | 0.0009 | 0.0067 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 0.0067 | 0.0000454 |

New Fargo | 0.0000454 | 0.0565 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 0.0134 | 0.0009454 |

New Fargo | 0.0009454 | 0.0498 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 0.5 | 0.953 |

New Fargo | 0.953 | 0.12 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 0.5 | 0.047 |

New Fargo | 0.047 | 0.88 |

**Part B**

B. Using the results from the previous problem (#2), how many car trips will there be?

Recall

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 9395 | 5606 |

New Fargo | 6385 | 15665 |

Origin\Destination | Dakotopolis | New Fargo |
---|---|---|

Dakotopolis | 4697 | 5339 |

New Fargo | 6511 | 1867 |