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(a) For each of the cost coefficients c;, 1 < j < 4, find the range of values for Ac, for which the above solution remains optimal. (b) For each of the resources b;, 1 sis 3, find the range of values for Ab; for which the above solution remains feasihle

(a) For each of the cost coefficients c;, 1 < j < 4, find the range of values for Ac, for which the above solution remains optimal. (b) For each of the resources b;, 1 sis 3, find the range of values for Ab; for which the above solution remains feasihle

Advanced Engineering Mathematics
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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After adding slack variables x5, X6, and x, and solving by the simplex method, 1. Consider the linear programming problem Maximize z = x+ 2x2 +X3 + X4 %3D subject to 2x1 + x2 + 3x3 + x4 5 8 + 4x4 s 12 2x1 + 3x2 s 18 3x1 + x2 + 2x3 x, 20 1sjs 4. we obtain the final tableau shown below. 1 CB X3 X5 X6 1 X3 1 X2 1 4 13 X7 1 28 (a) For each of the cost coefficients c;, 1 <j < 4, find the range of values for Ac, for which the above solution remains optimal. (b) For each of the resources b;, 1 sis 3, find the range of values for Ab, for which the above solution remains feasible. 2. What will be an optimal solution to the problem in Exercise 1 (a) if c, is changed to 3? (b) if b2 is changed to 26? (c) if cz is changed to ? (d) if b, is changed to 127? 1/91/9 Elo nla -/3 O N/3 1/3 1/9 •/m 0la 17
Transcribed Image Text:After adding slack variables x5, X6, and x, and solving by the simplex method, 1. Consider the linear programming problem Maximize z = x+ 2x2 +X3 + X4 %3D subject to 2x1 + x2 + 3x3 + x4 5 8 + 4x4 s 12 2x1 + 3x2 s 18 3x1 + x2 + 2x3 x, 20 1sjs 4. we obtain the final tableau shown below. 1 CB X3 X5 X6 1 X3 1 X2 1 4 13 X7 1 28 (a) For each of the cost coefficients c;, 1 <j < 4, find the range of values for Ac, for which the above solution remains optimal. (b) For each of the resources b;, 1 sis 3, find the range of values for Ab, for which the above solution remains feasible. 2. What will be an optimal solution to the problem in Exercise 1 (a) if c, is changed to 3? (b) if b2 is changed to 26? (c) if cz is changed to ? (d) if b, is changed to 127? 1/91/9 Elo nla -/3 O N/3 1/3 1/9 •/m 0la 17
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