Use big 𝑀 method solve. 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = 2𝑦1 + 4𝑦2 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 2𝑦1 – 3𝑦2 ≥ 2,
−𝑦1 + 𝑦2 ≥ 3; 𝑦1
, 𝑦2 ≥ 0
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜
After introducing surplus,artificial variables
Min Z=2x1+4x2+0S1+0S2+MA1+MA2
subject to
2x1-3x2-S1+A1=2-x1+x2-S2+A2=3
and x1,x2,S1,S2,A1,A2≥0
Positive maximum Zj-Cj is M-2 and its column index is 1. So, the entering variable is x1.
Minimum ratio is 1 and its row index is 1. So, the leaving basis variable is A1.
∴ The pivot element is 2.
Entering =x1, Departing =A1, Key Element =2
Since all Zj-Cj≤0
Hence, optimal solution is arrived with value of variables as :
x1=1,x2=0
Min Z=2
But this solution is not feasible
because the final solution violates the 2nd constraint - x1 + x2 ≥ 3.
and the artificial variable A2 appears in the basis with positive value 4
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