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

D
E
F

7
6
3

3
4
2

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

Asked by Topperlearning User | 12th Sep, 2014, 03:47: PM

Expert Answer:

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  | 12th Sep, 2014, 05:47: PM