Machine type |
Available time(in machine hours per week) |
---|---|

Milling machine | 500 |

Lathe | 350 |

Grinder | 150 |

The number of machine hours required for each unit of the respective products is

Machine type |
Product 1 |
Product 2 |
Product 3 |
---|---|---|---|

Milling machine | 9 | 3 | 5 |

Lathe | 5 | 4 | 0 |

Grinder | 3 | 0 | 2 |

The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be $30, $12, and $15, respectively, on products 1, 2, and 3. The objective is to determine how much of each product the firm should produce to maximize profit.

Formulate the linear programming model for this problem.