Ask Question, Ask an Expert


Ask Homework Help/Study Tips Expert

problem 1: Duality

Recall the max flow problem:


max x2t + x3t
xs1 = x12 + x13
xs2 + x12 = x2t
x13 = x3t

0 ≤ xs1 ≤ 2
0 ≤ xs2 ≤ 3
0 ≤ x12 ≤ 3
0 ≤ x13 ≤ 4
0 ≤ x2t ≤ 2
0 ≤ x3t ≤ 1

A) prepare the dual of the above max-flow problem.

B) Solve both problems with AMPL, and for each print the values of the variables and the values of the dual variables (if a problem has a constraint c1, its dual value can be displayed with the command “display c1.dual;”). Verify that the numbers correspond between primal and dual, and that the optimal solution of the primal and the dual is in accordance with duality.

C) Show the minimum cut that results from solving the dual problems.

D) Consider replacing the objective function in the max cut problem with max xs1 + xs2 which gives an equivalent formulation of the max-flow problem. How does the dual formulation change? describe why it is equivalent to the first dual problem.

problem 2: Complementary slackness and duality

Consider the following LP problem:

min x1 + 3x2 + x3 − x4
s.t. x1 + x2 + x3 + x4 ≥ 0
x1 + x2 − x3 − x4 ≥ 1
x2, x3 ≥ 0 x1, x4 ≤ 0.

A) Unique primal-dual solutions.

• Find a feasible solution (by trying a few guesses) and compute its associated value of the objective function, zprimal.

• prepare the dual.

• Find a feasible solution to the dual (just pick one) and compute its associated value of the objective function, zdual, and check, according to weak duality, that it is not less than zprimal.

• Solve the dual through the graphical method.

• After finding the optimal value of the dual variables, use complementary slackness to find the optimal value of the primal variables.

• Solve both primal and dual problems in AMPL. Print out the solutions.

B) Multiple primal solutions.

• Change the right hand side of the second constraint to -1. How would the dual change?

• Solve the new dual problem graphically.

• Again use complementarity to derive the primal solution. Do you get a unique primal solution or do you get more than one? Can you find all primal optimal solutions? (Hint: all feasible solutions that satisfy complementarity are optimal).

• Solve both primal and dual problems in AMPL. Print out the solutions.

• For the primal problem which of the multiple solutions do you obtain? Can you modify the primal problem a little to obtain a different solution from the optimal set?

problem 3: Linear Programming

Consider the following optimization problem:

min x
s.t. x ≥ max{a1, a2, . . . , an}

Reprepare this problem as a Linear Programming Problem. What is the solution of this problem? prepare the dual of this problem. From duality theory and complementary slackness give a simple formula for the optimal solution of the dual.

Homework Help/Study Tips, Others

  • Category:- Homework Help/Study Tips
  • Reference No.:- M91167

Have any Question? 

Related Questions in Homework Help/Study Tips

Cindy is a 34 year old single woman seeking counsel from

Cindy is a 34 year old single woman seeking counsel from you for her frustration and unhappiness in life. As you assess her story, you find out the following information: She is a CPA and works at a local accounting firm ...

Library research assignmentyour director has asked you to

Library Research Assignment Your director has asked you to create a white paper for dissemination to all supervising counselors. This paper is to address the following 2 different purposes: To provide all supervising cou ...

Write a paper 5-7 pages in apa format including at least 2

Write a paper (5-7 pages) in APA format (including at least 2 scholarly references) on the following: Discuss the mass media impacts that are related to your chosen product and the advertising campaign. Examine the campa ...

Bullpersonal choicesoverviewwrite a 3 page report in which

• Personal Choices Overview Write a 3 page report in which you examine ways to reduce your environmental impact. By successfully completing this assessment, you will demonstrate your proficiency in the following course c ...

Landlord-tenant lawlarry landlord has recently renovated an

Landlord-Tenant Law Larry Landlord has recently renovated an apartment and has put it on the market to be rented for $800.00 a month. Larry Landlord has been in business for approximately five (5) years and has had both ...

Action and adventure festivalcreate a 1050- to 1400-word

Action and Adventure Festival Create a 1,050- to 1,400-word proposal for a themed film festival. The theme could be anything from a specific genre, like the Western, to a topic, such as LGBTQ representations, to a specif ...

The politics of medicare and medicaidone of the significant

The Politics of Medicare and Medicaid One of the significant challenges for Medicare and Medicaid is not necessarily the implementation of the program but the influence of the political climate in regard to both the fina ...

Assignmentanalyze and brief one occupational safety and

Assignment Analyze and brief one Occupational Safety and Health Review Commission decisions by Administrative Law Judges or Commissioners. You can access these decisions from the Occupational Safety & Health Review Commi ...

Write a paper of no more that 750 words that serves as the

Write a paper of no more that 750 words that serves as the introduction to your Health and Safety Practices Plan. Identify an organization by choosing your organization or one you know, but the company you choose must pr ...

Memory please respond to the followingbriefly describe a

"Memory" Please respond to the following: Briefly describe a situation where you or another person remembered an experience or situation differently. Apply what you have learned in Chapter 7 in an analysis of why your me ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen