Answered: X2 X3 X6 15 0. 0. 0. -5 15 1. 0. 0. -1…

X2 X3 X6 15 0. 0. 0. -5 15 1. 0. 0. -1 x = 10 M = 5. 0. -1 0. 0. 1. 0. 10 -1 0. -1 Find the set of all optimal solutions to the linear program whose canonical form tableau

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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Question

X1
X2
X3
X5
X6
-5
0.
1.
0.
0.
0.
-1
0.
15
0.
0.
M =
10
0.
-1
0.
1.
10
-1
0.
-1
Find the set of all optimal solutions to the linear
program whose canonical form tableau

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Solve this LP max z = 3x1 + 2*2 + 2.5x3 8.t. has optimal tableau. So B = ā13 5₁ 1+ 2+ 2013 2x1 + 2x3 1, 2, 3 > 0 = 1; 1 1 0 2 and B-¹ = 15₂ 3 = <4 <6 and using B-¹ and B-¹cgy formulas the missing values in optimal tableau are C = 2.5; C = 3 ); 131 = 28 = 0 0; 1 1 2 0 11/123 and cay = 2 3 Z 21 1 0 0 0 0 1 2 Ty 81 0 Ts Ca 1 0 ā13 ā23 rhs Ž $2 1/2 1 -1/2 ₁ 0 1/2 5₂ and the optimal solution for zis z = 11 Now find the maximum amount A = 2.5 that the value of c can be increased so that the optimal BV remains optimal.
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nts in Page 348 This theorem simplifies the job of finding an optimum value. First, graph the feasible region and find all corner points. Then test each point in the objective function. Finally, identify the corner point producing the optimum solution. With the theorem, the problem in Example 1 could have been solved by identifying the five corner points of Figure 7.16: (0, 1), (0, 2), (.5, 2.25), (2, 0), and (1, 0). Then, sub- stituting each of these points into the objective function z = 2x + 5y would identify the corner points that produce the maximum and minimum values of z. Corner Point (0, 1) (0, 2) (.5, 2.25) (2,0) (1, 0) 2(0)+ 5(1) = 5 2(0)+ 5(2) = 10 2(.5) + 5(2.25) = 12.25 2(2) + 5(0) = 4 2(1) + 5(0) = 2 Value of z = 2x + 5y 348 ■ (maximum) From these results, the corner point (.5, 2.25) yields the maximum value of 12.25 and the cor- ner point (1, 0) gives the minimum value of 2. These are the same values found earlier. A summary of the steps for solving a linear programming…
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