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An oil company has two depots A and B with capacities 7000 and 4000 respectively. The company is to supply oil to three petrol pumps. D, E and F whose requirements are 4500 , 3000 and 3500 respectively. The distance (in km) between the depots and petrol pump is given as follows:   To/From A B DEF 763 342 How would the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?
Asked by Topperlearning User | 12 Sep, 2014, 03:47: PM

Problem can be represented as
Minimise z = 16x + 20y
st x + 2y  10
2x + 2y  12 or x + y  16
3x + y  8
x  0, y  0

 To/From A B D E F 7 6 3 3 4 2

Assuming that transportation cost of 10  of oil is Re 1.

 Corner Points A(3500, 0) B(4500, 0) C(4500, 2500) D(4000, 3000) E(500, 3000) z = 5000 z = 5300 z = 5550 z = 5450 z = 4400

Hence, minimum cost is Rs 4400, when
from depot A, 5000 is transported to D
3000 is transported to E
3500 is transported to F
from depot B 4000 is transported to D

Answered by | 12 Sep, 2014, 05:47: PM

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