Optimization Techn Industr Eng examJust please give me good answer for the file I attach. And you need to use excel to solve the last answer.
Final Exam
Instead of floating point arithmetic, it is recommended to do arithmetic with fractions. Solve the problems using the methods you learned in class (Optional ways you google will not earn any point).
NAME:
SIGN:
Total: /25
1-1
1-2
1-3
1-4
1-5
/0
/2
/2
/2
/3
2-1
2-2
2-3
2-4
3-1
/2
/2
/2
/3
/3
3-2
/4
1. We are solving the max flow problem.
1-1. (0 point) The initial flow is as follows with the flow value = 3.
Variable
Value
xs1
1
xs3
2
x12
0
x14
1
x32
2
x34
0
x2t
2
x4t
1
Flow Value =
3
1-2. (2 points) The residual network of the flow in 1-1 is illustrated as follows. Fill in the residual capacities in the table. Overdraw an augmenting path with the solid lines. What is the capacity of the augmenting path?
Arc
Residual Capacity
Arc
Residual Capacity
(s,1)
(1,s)
(s,3)
(3,s)
(1,2)
(2,1)
(1,4)
(4,1)
(3,2)
(2,3)
(3,4)
(4,3)
(2,t)
(t,2)
(4,t)
(t,4)
Capacity of the augmenting path = .
1-3. (2 points) What is the new flow augmented by the path flow in 1-2? (Fill in the blanks in the table on the right.) And, what is the new flow value?
Variable
Value
xs1
xs3
x12
x14
x32
x34
x2t
x4t
Flow Value =
1-4. (2 points) Fill in the blanks of the table with the residual capacities on the residual network of the new flow.
Arc
Residual Capacity
Arc
Residual Capacity
(s,1)
(1,s)
(s,3)
(3,s)
(1,2)
(2,1)
(1,4)
(4,1)
(3,2)
(2,3)
(3,4)
(4,3)
(2,t)
(t,2)
(4,t)
(t,4)
1-5. (2 points) Certify with a cut (S, T), s S and t T, that the new flow is optimal. Explicitly write the nodes of S and T, and overdraw the cut edges with solid lines on the figure. What is the cut capacity?
Answer: S = { }, T = { }, Cut Capacity = .
2. Perform the network simplex method to solve the minimum cost network flow problem beginning with the initial basis B = {xs2 = 3, x2t = 3, x1t = 5, x3t = 4}. The non-basic variables are xs1 = 5 and xs3 = 4, x21 = 0 and x23 = 0. In every iteration, dual variable πs = 0.
2-1. (2 points) Overdraw the initial basic arcs with the solid lines in the following figure. Calculate and write the dual variables. Calculate and write the reduced costs of the non-basic variables.
Dual variable
Value
πs
0
π1
π2
π3
πt
Non-basic variable
Value
Reduced cost
xs1
5
xs3
4
x21
0
x23
0
2-2. (2 points) Is the initial basis optimal? Circle (Yes/No) If No, overdraw with solid arcs the cycle along which the circular flow θ flows in the figure and fill in the blanks in the table.
Variable
Value
Basic/non-basic (B/N?)
Reduced Cost
Check the entering arc ( v )
Value update over the cycle (old ± θ = new)
Check the leaving arc and write the value of θ
xs2
3
B
0
x2t
3
B
0
x1t
5
B
0
x3t
4
B
0
xs1
5
N
xs3
4
N
x21
0
N
x23
0
N
2-3. (2 points) Overdraw the basic arcs with the solid lines in the following figure. Calculate and write the dual variables. Calculate and write the reduced costs of the non-basic variables.
Dual variable
Value
πs
0
π1
π2
π3
πt
Non-basic variable
Value
Reduced cost
2-4. (2 points) Is the basis optimal? Circle (Yes/No) If No, overdraw with solid arcs the cycle along which the circular flow θ flows in the figure and fill in the blanks in the table.
Variable
Value
Basic/non-basic (B/N?)
Reduced Cost
Check the entering arc ( v )
Value update over the cycle (old ± θ = new)
Check the leaving arc and write the value of θ
xs2
x2t
x1t
x3t
xs1
xs3
x21
x23
3. Consider the assignment problem with the following cost matrix C = ( cij ), where cij is the cost to assign worker i to job j.
5 8 7 3 2
4 3 3 7 5
4 8 5 3 3
3 6 5 2 5
2 7 5 6 8
3-1. (3 points) Explicitly write down an LP formulation of the assignment problem.
3-2. (4 points) Solve the problem using Excel Solver and submit your Excel Worksheet.
Get Professional Assignment Help Cheaply
Are you busy and do not have time to handle your assignment? Are you scared that your paper will not make the grade? Do you have responsibilities that may hinder you from turning in your assignment on time? Are you tired and can barely handle your assignment? Are your grades inconsistent?
Whichever your reason may is, it is valid! You can get professional academic help from our service at affordable rates. We have a team of professional academic writers who can handle all your assignments.
Our essay writers are graduates with diplomas, bachelor’s, masters, Ph.D., and doctorate degrees in various subjects. The minimum requirement to be an essay writer with our essay writing service is to have a college diploma. When assigning your order, we match the paper subject with the area of specialization of the writer.
Why Choose Our Academic Writing Service?
Plagiarism free papers
Timely delivery
Any deadline
Skilled, Experienced Native English Writers
Subject-relevant academic writer
Adherence to paper instructions
Ability to tackle bulk assignments
Reasonable prices
24/7 Customer Support
Get superb grades consistently
How It Works
1. Place an order
You fill all the paper instructions in the order form. Make sure you include all the helpful materials so that our academic writers can deliver the perfect paper. It will also help to eliminate unnecessary revisions.
2. Pay for the order
Proceed to pay for the paper so that it can be assigned to one of our expert academic writers. The paper subject is matched with the writer’s area of specialization.
3. Track the progress
You communicate with the writer and know about the progress of the paper. The client can ask the writer for drafts of the paper. The client can upload extra material and include additional instructions from the lecturer. Receive a paper.
4. Download the paper
The paper is sent to your email and uploaded to your personal account. You also get a plagiarism report attached to your paper.
Get Professional Assignment Help Cheaply
Are you busy and do not have time to handle your assignment? Are you scared that your paper will not make the grade? Do you have responsibilities that may hinder you from turning in your assignment on time? Are you tired and can barely handle your assignment? Are your grades inconsistent?
Whichever your reason may is, it is valid! You can get professional academic help from our service at affordable rates. We have a team of professional academic writers who can handle all your assignments.
Our essay writers are graduates with diplomas, bachelor’s, masters, Ph.D., and doctorate degrees in various subjects. The minimum requirement to be an essay writer with our essay writing service is to have a college diploma. When assigning your order, we match the paper subject with the area of specialization of the writer.
Why Choose Our Academic Writing Service?
Plagiarism free papers
Timely delivery
Any deadline
Skilled, Experienced Native English Writers
Subject-relevant academic writer
Adherence to paper instructions
Ability to tackle bulk assignments
Reasonable prices
24/7 Customer Support
Get superb grades consistently
How It Works
1. Place an order
You fill all the paper instructions in the order form. Make sure you include all the helpful materials so that our academic writers can deliver the perfect paper. It will also help to eliminate unnecessary revisions.
2. Pay for the order
Proceed to pay for the paper so that it can be assigned to one of our expert academic writers. The paper subject is matched with the writer’s area of specialization.
3. Track the progress
You communicate with the writer and know about the progress of the paper. The client can ask the writer for drafts of the paper. The client can upload extra material and include additional instructions from the lecturer. Receive a paper.
4. Download the paper
The paper is sent to your email and uploaded to your personal account. You also get a plagiarism report attached to your paper.
PLACE THIS ORDER OR A SIMILAR ORDER WITH Essay fount TODAY AND GET AN AMAZING DISCOUNT
The post Optimization Technology Industrial Engineering exam appeared first on Essay fount.
What Students Are Saying About Us
.......... Customer ID: 12*** | Rating: ⭐⭐⭐⭐⭐"Honestly, I was afraid to send my paper to you, but you proved you are a trustworthy service. My essay was done in less than a day, and I received a brilliant piece. I didn’t even believe it was my essay at first 🙂 Great job, thank you!"
.......... Customer ID: 11***| Rating: ⭐⭐⭐⭐⭐
"This company is the best there is. They saved me so many times, I cannot even keep count. Now I recommend it to all my friends, and none of them have complained about it. The writers here are excellent."
"Order a custom Paper on Similar Assignment at essayfount.com! No Plagiarism! Enjoy 20% Discount!"
