# linear programming

*label*Engineering

*timer*Asked: Apr 28th, 2017

**Question description**

Excel Problems

- A computer company has enough regular production capacity to produce 160 computers per week. It can produce an additional 50 computers per week with overtime. The cost of producing a computer during regular time is $190. The cost of producing a computer during overtime is $260. It costs $10 per week to hold a computer in inventory for future delivery. The orders anticipated over the next six weeks are:

Week | Computer orders |

1 | 110 |

2 | 170 |

3 | 230 |

4 | 180 |

5 | 150 |

6 | 245 |

Determine the regular and overtime production the company will need each week to meet its orders at minimum cost. The company wants no inventory left at the end of the six week period.

Please note that it does not have to produce exactly 160 per week during regular time. Your program must show that it could produce less than 160 computers.

Describe in one paragraph the sensitivity of the solution to the regular time production capacity, overtime capacity, regular production cost and overtime production cost.

- A petroleum company produces three grades of motor oil – super, premium, and extra from three components. The company wants to determine the optimal mix of the three components in each grade of motor oil that will maximize profit. The maximum quantities available of each component and their cost per barrel are as follows:

Component | Maximum, barrels available/day | Cost per barrel |

1 | 4,500 | $12 |

2 | 2,700 | $10 |

3 | 3,500 | $14 |

In order to ensure the appropriate blend, each grade has certain general specifications. Each grade must have a minimum amount of component 1 plus a combination of other components as follows:

Grade | Component specification | Selling price per barrel |

Super | At least 50% of component 1 Not more than 30% of component 2 | $23 |

Premium | At least 40% of component 1 Not more than 25% of component 3 | $20 |

Extra | At least 60% of component 1 At least 10% of component 2 | $18 |

The company wants to produce at least 3,000 barrels of each grade of motor oil.

Describe in one paragraph the sensitivity of the solution to the number of barrels of the components available and their cost.