Question

An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table:

Distance in (km)
From/To	A	B
D	7	3
E	6	4
F	3	2

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?

Answer 1

(ii) 3000 – y ≥ 0 = y ≤ 3000 

(iii) x + y – 3500 ≥ 0 = x+y ≥ 3500 x ≥ 0 

(iv) 7000 – (x + y) ≥ 0= x + y ≥ 3500 y ≥ 0

ABCD is the the solution region 

A (500, 3000) Z = Rs 4400 

B (3500,0) Z = Rs 5000 

C (4500,0) Z = Rs 5300 

D (4500, 2500) Z = Rs 5550 

E (4000,3000) Z = Rs 5450 

Z is minimised at (500,3000) 

i.e. Rs 4400 

From A to D 500 Ltrs 

From A to E 3000 Ltrs 

From A to F 3500 Ltrs 

From B to D 4000 Ltrs.