Question

An Oil Corporation has got three refineries P, Q and R and it has to send petrol to four different depots A, B, C and D. The cost of shipping 1 gallon of petrol from each refinery to each depot is given below. The requirements of the depots and the available petrol at the refineries are also given. Find the minimum cost of shipping after obtaining an initial solution by Vogel’s Approximation Method.

Answer 1

Explanation:

Corner

points

A (500,

3000)

LTE 2 4

Value of Z= 0.3X +

0.1Y + 3950

4400 (Minimum)

B (3500, 0) 5000

C (4500, 0) 5300

D (4500,

2500)

E (4000,

3000)

5550

5450

Hence minimum transportation cost is 4400 Rs. Transporter needs to supply as

follows:

Depot A to petrol pump D = X = 500 L

Depot A to petrol pump E=Y = 3000 L

Depot A to petrol pump F = 7000 - X -

Y = 3500 L

Depot B to petrol pump D= 4500 – X = 4000 L

Depot B to petrol pump E = 3000 – Y = 0 =