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2. Use the simplex algorithm to find an optimal solution to the following LP: max z 5x1 + 3x2 + x3 5x +3x2 +6x s 15
math   Statistics-And-Probability   
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Find solution using Simplex(BigM) method MAX Z5x1 +3x2 + x3 subject to x1 t x2 + 3x3 < 6 5x1 + 3x2 +6x3 < 15 and x1,x2,x3 >E 0 Solution: Problem is subject to 5x13x2 +6x3 s15 and x1, x2,x3 20; The problem is converted to canonical form by adding slack, surplus and artificial variables as appropiate 1. As the constraint-1 is of typeswe should add slack variable S 2. As the constraint-2 is of typewe should add slack variable S2 After introducing slack variables subject to xi+ x2 + 3x3 + Si 5 x1 3x2 + 6x3 and x1,X2.x3.31.32-Iteration-1 C, MinRatio 与 15 S, 15 -5↑ Negative minimum Z, - C, is-5 and its column index is 1. So, the entering variable is x Minimum ratio is 3 and its row index is 2. So, the leaving basis variable is S2 :. The pivot element is 5 Entering - x. Departing - S2. Key Element - +R2(new) - R2(old) 5 + R(new) R1(old) - R (new)Iteration-2 C, S. MinRatio Z= 15 Since all Z, - C 0 Hence, optimal solution is arrived with value of variables as Max Z = 15

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