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# 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 quintals form the godowns to the shops are given in following table To/Form A B D E F 6 3 2.5 4 2 3 How would the supplies be transported in order that the transportation cost is minimum. What is the minimum cost?

Asked by Topperlearning User 22nd September 2014, 10:45 AM

LPP can be represented diagram matically as

Using table cost of transportation

which is to be minimized
Also, we have the following constraints
60 – x  0, 50 – y  0
100 – (x + y)  0
x + y – 60  0
x  0, y  0
So, the LP can be stated as
Minimum z =
st x  60, y  50
x + y  100
x + y  60
x  0, y  0

 Corner Points Z = A(60, 0) B(60, 40) C(50, 50) D(10, 50) Z = 560 z = 620 z = 610 z = 510

Minimum cost of transportation is Rs 510.
When 10 quintals from godown A are sent to shop D.
50 quintals from A to E, 40 quintals from A to F, 50 quintals from B to D.

Answered by Expert 22nd September 2014, 12:45 PM
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