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