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 B X1 10 15 20 СВ X2 X3 S1 S2 b 20 X3 -1 1 -1/3 10 X1 1 -1 5 30 1 20 zj zj-cj | 0 10 10/3 10/3 100 15 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.
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.
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