Question

Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops are given in the following table: How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?

Transportation cost Per quintal (in Rs)
From/To	A	B
D	6	4
E	3	2
F	2.50	3

Answer 1

(i) 60 – x ≥ 0 ⇒ x ≤ 60 

(ii) 50 – y ≥0 ⇒ y ≤ 50 

(iii) 100 – (x + y) ≥ 0 ⇒ x + y ≤ 100 

(iv) x + y – 60 ≥ 0 ⇒ x + y ≥ 60

ABCD is the solution region

 A(10, 50) Z = Rs 510 

B(50, 50) Z = Rs 610 

C (60, 40) Z = Rs 620 

D (60, 0) Z = Rs 560 

Cost is minimised to Rs 510 at A (10,50)