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

College Algebra
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ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
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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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