# Susan Helms Manufacturing Co. has hired you to analyze its shipping costs from the existing three factories

## Question:

Susan Helms Manufacturing Co. has hired you to analyze its shipping costs from the existing three factories to five warehouses. These factories have produced 1900, 1420, and 2050 units, respectively, and these units will be all shipped out to the warehouses. There are five warehouses, each located in a different region. According to the sales in the retail stores in these five regions, the minimum demands each warehouse is expected to meet are 900, 1500, 600, 800, and 1100 units, respectively, for next month. The table below shows the information on the above-mentioned demands and produced units, and freight costs (per unit) between each factory and each warehouse.

Due to the recent active markets, the management indicated that the warehouse should plan its orders to the factories to receive at least 20% more than the minimum demand it has to meet. If it is not possible for all warehouses to meet this expectation, you should have as many warehouses as possible that meet such expectations. With the above management's expectation, what is the most shipping cost-effective shipping schedule (showing the shipping quantities on each shipping lane, i.e., the cells below in cream color) for next month? What is the resulting shipping cost from this optimal solution? (A solver is required)

TABLE | ||||||

Warehouse 1 | Warehouse 2 | Warehouse 3 | Warehouse 4 | Warehouse 5 | Units to ship out | |

Factory 1 | $7 | $10 | $8 | $12 | $14 | 1900 |

Factory 2 | $9 | $8 | $11 | $8 | $10 | 1420 |

Factory 3 | $10 | $9 | $9 | $8 | $11 | 2050 |

Min. demand | 900 | 1500 | 600 | 800 | 1100 |

Warehouse 1 | Warehouse 2 | Warehouse 3 | Warehouse 4 | Warehouse 5 | |

Factory 1 | |||||

Factory 2 | |||||

Factory 3 |

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