Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Given the LP model
Maximize Z =10 x1 +15x2 +20x3
Subject to
2 x1+4 x2+6 x3≤24
3 x1+9 x2+6 x3≤30
x1, x2, x3≥0
The optimal table is

           Cj   10      15      20     0        0
CB      B     X1     X2     X3    S1      S2     b
20      X3    0      -1        1      ½      -1/3   2
10      X1    1       5        0     -1         1      6
          zj    10      30      20     0     10/3  100
     zj-cj      0       15       0      0     10/3

a. Find the range of objective function coefficient c2 of variable x2 such that the optimality is unaffected.
b. Find the range of the objective function coefficient c1 of variable x1 such that the optimality is unchanged.

c. Check whether the optimality is affected, if the profit coefficients are changed from (10, 15, and 20) to (8, 27, and 15). If so, find the revised optimal solution.

4. Given the LP model
Maximize Z =10 x1 +15x2 +20x3
Subject to
2 x1+4 x2+6 x3524
3 x1+9 x2+6 x3530
X1, X2, X320
The optimal table is
Ci
В
10
15
20
CB
X1
X2
X3
S1
S2
20
-1/3
2
6
X3
-1
1
10
X1
1
-1
1
10
30
20
zi
zj-cj | 0
10/3
100
15
10/3
a. Find the range of objective function coefficient c2 of variable x2 such that the
optimality is unaffected.
b. Find the range of the objective function coefficient c1 of variable x1 such that the
optimality is unchanged.
c. Check whether the optimality is affected, if the profit coefficients are changed
from (10, 15, and 20) to (8, 27, and 15). If so, find the revised optimal solution.
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Transcribed Image Text:4. Given the LP model Maximize Z =10 x1 +15x2 +20x3 Subject to 2 x1+4 x2+6 x3524 3 x1+9 x2+6 x3530 X1, X2, X320 The optimal table is Ci В 10 15 20 CB X1 X2 X3 S1 S2 20 -1/3 2 6 X3 -1 1 10 X1 1 -1 1 10 30 20 zi zj-cj | 0 10/3 100 15 10/3 a. Find the range of objective function coefficient c2 of variable x2 such that the optimality is unaffected. b. Find the range of the objective function coefficient c1 of variable x1 such that the optimality is unchanged. c. Check whether the optimality is affected, if the profit coefficients are changed from (10, 15, and 20) to (8, 27, and 15). If so, find the revised optimal solution.
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