2. Chapter 14 Review 45: Calculate ∂z∂x , where xez + zey = x + y.
Find the production schedule for the technology matrix and demand vector given below:
A= 0.1 0.3 0 D= 9
0.1 0.2 0.1 6
0.2 0.2 0.1 8
X= ?
?
?
Given the LP modelMaximize Z =10 x1 +15x2 +20x3 Subject to 2 x1+4 x2+6 x3≤243 x1+9 x2+6 x3≤30x1, x2, x3≥0The optimal table is
Cj 10 15 20 0 0 CB B X1 X2 X3 S1 S2 b20 X3 0 -1 1 ½ -1/3 210 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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