## 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
$30 \times 60+10 \times 75+15 \times 65+35 \times 70=5975.$