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Assuming that the transportation cost of 10 litres of oil is Re 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?
Asked by Vishnu Last Modified
Answer 
Vishaka Bhutia
Home Tutor
Let x and y litres of oil be supplied from A to the petrol pumps, D and E. Then, (7000 − x − y) will be supplied from A to petrol pump F.
The requirement at petrol pump D is 4500 L. Since x L are transported from depot A, the remaining (4500 −x) L will be transported from petrol pump B.
Similarly, (3000 − y) L and 3500 − (7000 − x − y) = (x + y − 3500) L will be transported from depot B to petrol pump E and F respectively.
The given problem can be represented diagrammatically as follows.
Cost of transporting 10 L of petrol = Re 1
Cost of transporting 1 L of petrol = 
Therefore, total transportation cost is given by,
The problem can be formulated as follows.
Minimize z = 0.3x + 0.1y + 3950 … (1)
subject to the constraints,
The feasible region determined by the constraints is as follows.
The corner points of the feasible region are A (3500, 0), B (4500, 0), C (4500, 2500), D (4000, 3000), and E (500, 3000).
The values of z at these corner points are as follows.
| Corner point | z = 0.3x + 0.1y + 3950 | |
| A (3500, 0) | 5000 | |
| B (4500, 0) | 5300 | |
| C (4500, 2500) | 5550 | |
| D (4000, 3000) | 5450 | |
| E (500, 3000) | 4400 | → Minimum |
The minimum value of z is 4400 at (500, 3000).
Thus, the oil supplied from depot A is 500 L, 3000 L, and 3500 L and from depot B is 4000 L, 0 L, and 0 L to petrol pumps D, E, and F respectively.
The minimum transportation cost is Rs 4400.
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