Two godowns A and B have grain 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.

6. Two godowns A and B have grain 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 is given in the following table:

Transportation cost per quintal (in Rs)

From/To A B

D 6 4

E 3 2

F 2.50 3

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

Answers (1)

Let godown A supply x and y quintals of grain to shops D and E respectively. Then, (100-x-y) will be supplied to shop F. Requirements at shop D is 60 since godown A supplies x . Therefore, the remaining (60-x) quintals of grain will be transported from godown B.

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