Consider the following IP: Z max s.t. X1 2x1 + 3x2 2x1 + x2 x13x₂ < 12 < 15 x1 - x2 <9 x = Z² The optimal tableau (for the Linear Relaxation) is +0.6x3 +0.824 +0.6x3 -0.2x4 X2 -0.2x3 +0.4x4 0.6x3 −0.824 = +x5 = 19.2 4.2 3.6 8.4 where x3, x4, 5 are slack variables (i.e., x3 = 12 – 2x1 x2 and x4, x5 are similarly defined). (a) Which variable(s) (choose from {x₁,x2}) could branch-and-bound branch on? Why? (b) For every variable in your answer to part a, list all the constraints that may be added when branching on that variable. (c) Find two Gomory fractional cuts based on the first two constraints in the optimal tableau (for this step, you are allowed to use all of the variables including the slack variables in the expressions for the cuts). (d) Express the cuts you found in part c in the original space (i.e., in terms of x1, x₂).
Consider the following IP: Z max s.t. X1 2x1 + 3x2 2x1 + x2 x13x₂ < 12 < 15 x1 - x2 <9 x = Z² The optimal tableau (for the Linear Relaxation) is +0.6x3 +0.824 +0.6x3 -0.2x4 X2 -0.2x3 +0.4x4 0.6x3 −0.824 = +x5 = 19.2 4.2 3.6 8.4 where x3, x4, 5 are slack variables (i.e., x3 = 12 – 2x1 x2 and x4, x5 are similarly defined). (a) Which variable(s) (choose from {x₁,x2}) could branch-and-bound branch on? Why? (b) For every variable in your answer to part a, list all the constraints that may be added when branching on that variable. (c) Find two Gomory fractional cuts based on the first two constraints in the optimal tableau (for this step, you are allowed to use all of the variables including the slack variables in the expressions for the cuts). (d) Express the cuts you found in part c in the original space (i.e., in terms of x1, x₂).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please give detailed explanation
Transcribed Image Text:Consider the following IP:
Z
max
s.t.
X1
2x1 + 3x2
2x1 + x2
x13x₂
< 12
< 15
x1 - x2
<9
x = Z²
The optimal tableau (for the Linear Relaxation) is
+0.6x3 +0.824
+0.6x3
-0.2x4
X2 -0.2x3
+0.4x4
0.6x3 −0.824
=
+x5 =
19.2
4.2
3.6
8.4
where x3, x4, 5 are slack variables (i.e., x3 = 12 – 2x1
x2 and x4, x5 are similarly defined).
(a) Which variable(s) (choose from {x₁,x2}) could branch-and-bound branch on? Why?
(b) For every variable in your answer to part a, list all the constraints that may be added when
branching on that variable.
(c) Find two Gomory fractional cuts based on the first two constraints in the optimal tableau (for this
step, you are allowed to use all of the variables including the slack variables in the expressions for
the cuts).
(d) Express the cuts you found in part c in the original space (i.e., in terms of x1, x₂).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 30 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
