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 Sep, 2014, 10:45: AM

Expert Answer:

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  | 22nd Sep, 2014, 12:45: PM