Midterm 2, 5 problems, 15 points each. Return this page.

Solve linear programs where all

-3 | x_{1} | 2 | x_{3} | Problem 1 |

1 | 2 | 3 | 4 | = x_{1} |

x_{2} | 0 | -x_{1} | 1 | =- x_{4} |

0 | 1 | 2 | 3 | -> min |

Answer: LP is infeasible.

2 | x_{2} | 3 | -x_{1} | Problem 2 |

1 | 2 | 3 | 4 | =- x_{1} |

x_{3} | 6 | 7 | 0 | = x_{4} |

0 | 1 | 2 | 3 | -> min |

Answer: LP is unbounded

-2 | x_{2} | 3 | -x_{3} | Problem 3 |

1 | -2 | -3 | 4 | = x_{1} |

-5 | 0 | 1 | 1 | = x_{1} |

0 | 1 | -2 | 3 | -> max |

Answer: LP is infeasible.

x_{3} | x_{2} | 3 | -x_{3} | Problem 4 |

1 | 2 | 3 | 4 | = x_{1} |

5 | 1 | 0 | -1 | = x_{4} |

0 | 1 | -2 | 3 | -> min |

Answer: LP is unbounded

0 | x_{2} | 1 | -x_{3} | Problem 5 |

0 | -1 | 3 | 0 | = x_{1} |

5 | 6 | -1 | -1 | = x_{2} |

0 | 1 | 2 | 0 | -> min |

min = 2 at