The dual of the above L.P.P. can be written as
Max ZD = 10W1 + 24W2
S.T.
W1 + 3W2 ≤ 20
W1 + 2W2 ≤ 10
W1, W2 ≥ 0
By using slack variables convert the problem into standard form, we have
Max Z = 10W1 + 24W2 + 0S1 + 0S2
S.T. W1 + 3W2 + S1 = 20
W1 + 2W2 + S2 = 10
W1, W2, S1, S2 ≥ 0
Initial basic feasible solution is given by
W1 = W2 = 0, S1 = 20, S2 = 10
Now prepare initial simplex table, we have
Converting the key element 2 as unity and then taking R1 → R1 – 3R2, we have
Here, all values of Zj – Cj ≥ 0. Hence, optimum solution exists, i.e.,
Min Z = 120, x1 = 0, x2 = 12
