north west corner rulestep1 the first

Question

North West Corner Rule:

Step1: The  first  assignment is made in  the cell  occupying  the upper  left  hand ( north  west ) corner  of  the transportation  table. The maximum  possible  amount is  allocated there. That is  X₁₁ min ( aa1 , b1)  this value  of X₁₁  is then  entered in  the  cell  ( 1, 1)  of the transportation table.

Step 2 :

a.       If b1>  a₁ move vertically downwards to the second row and make the second allocation  of  amount X₂₁ = min ( a₁ b₁- X₁₁) in the cell ( 2,1,).

b.      If  b₁ < a₁ move horizontally right  side  to the second column and make the second  allocation of  amount X₁₂  min ( a₁- X₁₁ , b₂ ) in the cell (1,2).

c.       If b₁ = a₁ there is a tie for the second allocation . one  can make  the second  allocation of  magnitude X₁₂ = min ( a₁- a₁, b₂ ) = 0 in the  cell ( 1,2) or X21 = min ( a₂ b₁- b₁) = o in the  cell ( 2,1)

Step 3: Start from the new  north  west  corner  of the transportation table  and repeat steps 1 an d2 until  all the  requirements  are satisfied.