Question: Consider the following LP problem and its optimal final tableau shown below: (LP): max z = 2x1 + x2 x3 s.t. x1 + 2x2 +

Consider the following LP problem and its optimal final tableau shown below: (LP): max z = 2x1 + x2 x3 s.t. x1 + 2x2 + x3 8 -x1 + x2 2x3 4 x1, x2, x3 0 Basic x1 x2 x3 x4 x5 RHS z 0 3 x1 1 2 1 1 0 x5 0 3 -1 1 1 x4 and x5 are slack variables in the 1st.., and 2 nd. constraints respectively, a) Fill out the empty cells in the given optimal simplex tableau. b) What is the optimality range for c1 ? c) What is the feasibility range for b2 ? d) If the coefficient of x2 in the objective function is changed from 1 to 3, calculate the corresponding changes, detemine whether the current optimum is changed? Consider the following LP problem and its optimal final tableau shown below:

(LP):maxz=2x1+x2x3s.t.x1+2x2+x38x1+x22x34x1,x2,x30 x4 and x5 are slack variables in the 1st.., and 2nd. constraints respectively, a) Fill out the empty cells in the given optimal simplex tableau. b) What is the optimality range for c1 ? c) What is the feasibility range for b2 ? d) If the coefficient of x2 in the objective function is changed from 1 to 3 , calculate the corresponding changes, detemine whether the current optimum is changed

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