QUESTION 1
Minimize Z = 36 X1A + 24X1B + 10X1C + 20X1D – PLANT 1
+ 30X2A + 20X2B + 8 X2C + 17X2D – PLANT 2
+ 45X3A + 30X3B + 13X3C + 25X3D – PLANT 3
Subject to
X1A + X1B + X1C + X1D = 1,000000
X2A + X2B + X2C + X2D = 1,200000
X3A + X3B + X3C + X3D = 800,000
X1A + X2A + X3A + X4A = 900, 000
X1B + X2B + X3B + X4B = 800, 000
X1C + X2C + X3C + X4C = 500,000
X1D + X2D + X3D + X4D = 800, 000
The minimum cell cost initial basic feasible solution
SOURCE
A
B
C
D
SUPPLY
PLANT 1
36
24
10
20
1000000
PLANT 2
30
20
8
17
1200000
PLANT 3
45
30
13
25
800000
Demand
900,000
800,000
500,000
800,000
3000000
To develop the path for the stepping-stone we allocate arbitrary zero to cell X1D
QUESTION 2
Minimize Z=
2X1A + 2X1B + 3X1C + 12X1D + 30X1E + 4X1F + 30X1G + 24X1H – PLANT 1
+ X2A + 6X2B + 2X2C + 6X2D + 15X2E + 2X2F + 15X2G + 12X2H – PLANT 2
+ X3A + 8X3B + 2X3C + 8X3D + 19X3E + 3X3F + 19X3G + 15X3H – PLANT 3
+ 3X4A + 20X4B + 5X4C + 20X4D + 50X2E + 7X4F + 50X4G + 40X4H – PLANT 4
Subject to
X1A + X1B + X1C + X1D + X1E + X1F + X1G+ X1H = 500000
X2A + X2B + X2C + X2D + X2E + X2F + X2G+ X2H = 1000000
X3A + X3B + X3C + X3D + X3E + X3F + X3G+ X3H = 800, 000
X4A + X4B + X4C + X4D + X4E + X4F + X4G+ X4H = 300, 000
X1A + X2A + X3A + X4A + X5A + X6A + X7A + X8A = 100, 000
X1B + X2B + X3B + X4B + X5B + X6B + X7A + X8A = 200, 000
X1C + X2C + X3C + X4C + X5C + X6C + X7C + X8C = 300,000
X1D + X2D + X3D + X4D + X5D + X6D + X7D + X8D = 400, 000
X1E + X2E + X3E + X4E + X5E + X6E + X7E + X8E = 600, 000
X1F + X2F + X3F + X4F + X5F + X6F + X7F + X8F = 200, 000
X1G + X2G + X3G + X4G + X5G + X6G + X7G + X8G = 500, 000
X1H + X2H + X3H + X4H + X5H + X6H + X7H + X8H = 300, 000
Using the minimum cell cost for the below transportation table we obtain
SOURCE
A
B
C
D
…