## Minimum Cell Method

A company has two factories A and B, and three warehouses X, Y and Z. Factories A and B make 40 and 50 widgets per month respectively. Warehouses X, Y and Z store 15, 45 and 30 widgets respectively. The cost of transporting from a particular factory to a particular warehouse is shown in the table below.

Factory\Warehouse | X | Y | Z | |

A | 80 | 75 | 60 | 40 |

B | 65 | 70 | 75 | 50 |

| 15 | 45 | 30 | |

The minimum cell method tries to minimise the cost by allocating the maximum throughput to the lowest cost options. The lowest cost options are in order, A-Z, B-X, B-Y, B-Z=A-Y, A-X.

We can allocate 30 units to option A-Z, 15 units to option B-X, 10 units to A-Y and 35 units to By.

Factory\Warehouse | X | Y | Z | |

A | 0 | 10 | 30 | 40 |

B | 15 | 35 | 0 | 50 |

| 15 | 45 | 30 | |

The total cost is \[30 \times 60+10 \times 75+15 \times 65+35 \times 70=5975.\]

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