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.What should the supplies be transported in order that the transportation cost is minimum?What is the minimum cost?

Answer 1

Let godown A supply x and y quintals of grain to shop D and E. Than godown A supply 100 – (x + y) quintals to shop F
⇒ x ≥ 0, y ≥ 0 and 100 – (x + y) ≥ 0
⇒ x ≥ 0, y ≥ 0 and x + y ≤ 100 ... (1)
also godown B supplies (60 – x), (50 – y) and 40 – (100 – (x + y)) quintals of grain to shop D, E and F
⇒ 60 – x ≥ 0, 50 – y ≥ 0 and x + y – 60 ≥ 0
⇒ x ≤ 60, y ≤ 50 and x+ y ≥ 60 ... (2)
Thus total transportation cost z is given by
z = 6x + 3y + 2.5 (100 – x – y) + 4 (60 – x) + 2 (50 – y) + 3 (x + y – 60)
⇒ z = 6x + 3y + 250 – 2.5x – 2.5y + 240 – 4x + 100 – 2y + 3x + 3y – 180
⇒ z = 2.5x + 1.5y + 410 ... (3)
Hence (1), (2), (3) are the required equations.

Answer 2

right @TheViper

Answer 3

right @jiteshmeghwal9

Answer 4

right @maheshmeghwal9

Answer 5

ok @JOYAL

Answer 6

right @mayankdevnani :)

Answer 7

right @ajprincess