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)