Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
4th Edition
ISBN: 9780534423551
Author: Wayne L. Winston
Publisher: Cengage Learning
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Expert Solution & Answer
Chapter 6.4, Problem 13P
Explanation of Solution
100% Rule for right-hand sides:
- Consider an LP that contains two constraints and right –hand sides
- The current basis is known to be optimal for
- Define,
- In here, maximum allowable increase is
- In here, maximum allowable increase is
- In here, maximum allowable decrease is
- In here, maximum allowable decrease is
- This stands for change in
- This stands for change in
- This stands for change in
- This stands for change in
- Thus,
- And
- Where,
- As the original LP has attained the optimal basis, the current basis remains optimal as long as the right-hand side of each constraint in the optimal table is non-negative.
- It is given that
- Hence, it is possible to write,
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The monotone restriction (MR) on the heuristic function is defined as
h (nj ) 2 h (ni ) - c (ni , nj ).
Please prove the following:
1. If h(n)
Consider the set 6x +12y + 4z = 70, 7x - 2y + 3z = 5, and 2x + 8y9z = 6. Determine the best option for performing left division on these linear algebraic equations.
Multiple Choice
A = [6, 12, 4; 7, -2, 3; 2, 8, -9];
B = [70; 5; 64];
Solution = A/B
A = [6, 12, 4; 7, -2, 3; 2, 8, -9];
B = [70; 5; 64];
Solution A\B
A = [6, 12, 4; 7, -2, 3; 2, 8, -9];
B = [70, 5, 64];
Solution A/B
A = [6, 12, 4; 7, -2, 3; 2, 8, -9];
B = [70, 5, 64];
Solution A\B
Will the solution be different if we use <= for the first three constraints?
MIN:
21X14+ 50X15+ 40X16+ 35X24+ 30X25+ 22X25+
55X+ 20X35+ 25X36
34
Subject to:
X14+ X15+ X16 = 275,000
X24+ X25+ X26 = 400,000
X34+ X35+ X36 = 300,000
X14+ X24+ X34 < 200,000
X15+ X25+ X35 < 600,000
X16+ X26+ X36 5 225,000
X14, X15, X16, X24, X25, X26, X34, X35, X3620
%3D
The solution will be the same
The solution will change
O We can' tell
Chapter 6 Solutions
Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
Ch. 6.1 - Prob. 1PCh. 6.1 - Prob. 2PCh. 6.1 - Prob. 3PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.3 - Prob. 3P
Ch. 6.3 - Prob. 4PCh. 6.3 - Prob. 5PCh. 6.3 - Prob. 6PCh. 6.3 - Prob. 7PCh. 6.3 - Prob. 8PCh. 6.3 - Prob. 9PCh. 6.4 - Prob. 1PCh. 6.4 - Prob. 2PCh. 6.4 - Prob. 3PCh. 6.4 - Prob. 4PCh. 6.4 - Prob. 5PCh. 6.4 - Prob. 6PCh. 6.4 - Prob. 7PCh. 6.4 - Prob. 8PCh. 6.4 - Prob. 9PCh. 6.4 - Prob. 10PCh. 6.4 - Prob. 11PCh. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.5 - Prob. 1PCh. 6.5 -
Find the duals of the following LPs:
Ch. 6.5 - Prob. 3PCh. 6.5 - Prob. 4PCh. 6.5 - Prob. 5PCh. 6.5 - Prob. 6PCh. 6.6 - Prob. 1PCh. 6.6 - Prob. 2PCh. 6.7 - Prob. 1PCh. 6.7 - Prob. 2PCh. 6.7 - Prob. 3PCh. 6.7 - Prob. 4PCh. 6.7 - Prob. 5PCh. 6.7 - Prob. 6PCh. 6.7 - Prob. 7PCh. 6.7 - Prob. 8PCh. 6.7 - Prob. 9PCh. 6.8 - Prob. 1PCh. 6.8 - Prob. 2PCh. 6.8 - Prob. 3PCh. 6.8 - Prob. 4PCh. 6.8 - Prob. 5PCh. 6.8 - Prob. 6PCh. 6.8 - Prob. 8PCh. 6.8 - Prob. 9PCh. 6.8 - Prob. 10PCh. 6.8 - Prob. 11PCh. 6.9 - Prob. 1PCh. 6.9 - Prob. 2PCh. 6.9 - Prob. 3PCh. 6.10 - Prob. 1PCh. 6.10 - Prob. 2PCh. 6.10 - Prob. 3PCh. 6.11 - Prob. 1PCh. 6.11 - Prob. 3PCh. 6.11 - Prob. 4PCh. 6.12 - Prob. 5PCh. 6.12 - Prob. 6PCh. 6.12 - Prob. 7PCh. 6 - Prob. 1RPCh. 6 - Prob. 2RPCh. 6 - Prob. 3RPCh. 6 - Prob. 4RPCh. 6 - Prob. 5RPCh. 6 - Prob. 6RPCh. 6 - Prob. 7RPCh. 6 - Prob. 8RPCh. 6 - Prob. 9RPCh. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 13RPCh. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 17RPCh. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - Prob. 25RPCh. 6 - Prob. 29RPCh. 6 - Prob. 33RPCh. 6 - Prob. 34RPCh. 6 - Prob. 35RPCh. 6 - Prob. 36RPCh. 6 - Prob. 37RP
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