Two godowns A and B have gram capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D. E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops are given in the following table:


How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?

Explanation

Solution :

Let godown A supply x and y quintals of grain to the shops D and E respectively. Then, `(100 − x − y)` will be supplied to shop F.

The requirement at shop D is `60` quintals since x quintals are transported from godown A.

Hence, the remaining `(60 −x)` quintals will be transported from godown B. Similarly, `(50 − y)` quintals and `40 − (100 − x − y) = (x + y − 60)` quintals will be transported from godown B to shop E and F respectively. The given problem can be represented diagrammatically as follows.






Total transportation cost z is given by,

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