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Q4. Consider the following LP problem and its optimal final tableau shown below: (LP): max z = 2x1 + x2-x3 Basic x1x2 x3 x4 x5 RHS s.t. x1 + 2x2 + x3 ≤8 Z 0 3 -x1 + x2-2x3 ≤4 x1 12 1 1 x1, x2, x3 20 x5 0 3 -1 1 x4 and x5 are slack variables in the 1*., and 2nd constraints respectively, Fill out the empty cells in the given optimal simplex tableau. b) What is the optimality range for c, ? a) 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? 0 1

Q4. Consider the following LP problem and its optimal final tableau shown below: (LP): max z = 2x1 + x2-x3 Basic x1x2 x3 x4 x5 RHS s.t. x1 + 2x2 + x3 ≤8 Z 0 3 -x1 + x2-2x3 ≤4 x1 12 1 1 x1, x2, x3 20 x5 0 3 -1 1 x4 and x5 are slack variables in the 1*., and 2nd constraints respectively, Fill out the empty cells in the given optimal simplex tableau. b) What is the optimality range for c, ? a) 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? 0 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q4. Consider the following LP problem and its optimal final tableau shown below: (LP): max z = 2x1 + x2-x3 Basic x1 x2 x3 x4 x5 RHS s.t. Z 0 3 x1 + 2x2 + x3 ≤8 -x1 + x2-2x3 ≤4 x1 12 1 x1, x2, x3 20 x5 0 3 -1 x4 and x5 are slack variables in the 1s., and 2nd constraints respectively, a) Fill out the empty cells in the given optimal simplex tableau. b) What is the optimality range for c, ? What is the feasibility range for b₂ ? 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? c) d) 1 1 0 1
Transcribed Image Text:Q4. Consider the following LP problem and its optimal final tableau shown below: (LP): max z = 2x1 + x2-x3 Basic x1 x2 x3 x4 x5 RHS s.t. Z 0 3 x1 + 2x2 + x3 ≤8 -x1 + x2-2x3 ≤4 x1 12 1 x1, x2, x3 20 x5 0 3 -1 x4 and x5 are slack variables in the 1s., and 2nd constraints respectively, a) Fill out the empty cells in the given optimal simplex tableau. b) What is the optimality range for c, ? What is the feasibility range for b₂ ? 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? c) d) 1 1 0 1
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