Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 6.7, Problem 7P
Program Plan Intro
Dual of Linear
The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.
- Every variable in the primal Linear Programming becomes a constraint in the dual LP.
- Every limit in the primal Linear Programming becomes a variable in the dual LP.
- In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.
Weak Duality:
- The weak duality is an optimization concept that states that the gap in duality is always greater than or equal to 0.
- This means the solution to the primary(minimization) problem is always greater than or equal to the solution to a dual problem associated with it.
Explanation of Solution
b.
Validity of the form of Lemma 3:
For showing validity of form of Lemma 3, it need to show that the dual is feasible and this will imply that the primal is bounded.
Assuming that the dual is to be feasible, let
Then Weak Duality implies that
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Modular Program Structure. Analysis of Structured Programming Examples. Ways to Reduce Coupling.
Based on the given problem, create an algorithm and a block diagram, and write the program code:
Function: y=xsinx
Interval: [0,π]
Requirements:
Create a graph of the function.
Show the coordinates (x and y).
Choose your own scale and show it in the block diagram.
Create a block diagram based on the algorithm.
Write the program code in Python.
Requirements:
Each step in the block diagram must be clearly shown.
The graph of the function must be drawn and saved (in PNG format).
Write the code in a modular way (functions and the main part should be separate).
Please explain and describe the results in detail.
Based on the given problem, create an algorithm and a block diagram, and write the program code:
Function: y=xsinx
Interval: [0,π]
Requirements:
Create a graph of the function.
Show the coordinates (x and y).
Choose your own scale and show it in the block diagram.
Create a block diagram based on the algorithm.
Write the program code in Python.
Requirements:
Each step in the block diagram must be clearly shown.
The graph of the function must be drawn and saved (in PNG format).
Write the code in a modular way (functions and the main part should be separate).
Please explain and describe the results in detail.
Based on the given problem, create an algorithm and a block diagram, and write the program code:
Function: y=xsinx
Interval: [0,π]
Requirements:
Create a graph of the function.
Show the coordinates (x and y).
Choose your own scale and show it in the block diagram.
Create a block diagram based on the algorithm.
Write the program code in Python.
Requirements:
Each step in the block diagram must be clearly shown.
The graph of the function must be drawn and saved (in PNG format).
Write the code in a modular way (functions and the main part should be separate).
Please explain and describe the results in detail.
Chapter 6 Solutions
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- Question: Based on the given problem, create an algorithm and a block diagram, and write the program code: Function: y=xsinx Interval: [0,π] Requirements: Create a graph of the function. Show the coordinates (x and y). Choose your own scale and show it in the block diagram. Create a block diagram based on the algorithm. Write the program code in Python. Requirements: Each step in the block diagram must be clearly shown. The graph of the function must be drawn and saved (in PNG format). Write the code in a modular way (functions and the main part should be separate). Please explain and describe the results in detail.arrow_forward23:12 Chegg content://org.teleg + 5G 5G 80% New question A feed of 60 mol% methanol in water at 1 atm is to be separated by dislation into a liquid distilate containing 98 mol% methanol and a bottom containing 96 mol% water. Enthalpy and equilibrium data for the mixture at 1 atm are given in Table Q2 below. Ask an expert (a) Devise a procedure, using the enthalpy-concentration diagram, to determine the minimum number of equilibrium trays for the condition of total reflux and the required separation. Show individual equilibrium trays using the the lines. Comment on why the value is Independent of the food condition. Recent My stuff Mol% MeOH, Saturated vapour Table Q2 Methanol-water vapour liquid equilibrium and enthalpy data for 1 atm Enthalpy above C˚C Equilibrium dala Mol% MeOH in Saturated liquid TC kJ mol T. "Chk kot) Liquid T, "C 0.0 100.0 48.195 100.0 7.536 0.0 0.0 100.0 5.0 90.9 47,730 928 7,141 2.0 13.4 96.4 Perks 10.0 97.7 47,311 87.7 8,862 4.0 23.0 93.5 16.0 96.2 46,892 84.4…arrow_forwardYou are working with a database table that contains customer data. The table includes columns about customer location such as city, state, and country. You want to retrieve the first 3 letters of each country name. You decide to use the SUBSTR function to retrieve the first 3 letters of each country name, and use the AS command to store the result in a new column called new_country. You write the SQL query below. Add a statement to your SQL query that will retrieve the first 3 letters of each country name and store the result in a new column as new_country.arrow_forward
- We are considering the RSA encryption scheme. The involved numbers are small, so the communication is insecure. Alice's public key (n,public_key) is (247,7). A code breaker manages to factories 247 = 13 x 19 Determine Alice's secret key. To solve the problem, you need not use the extended Euclid algorithm, but you may assume that her private key is one of the following numbers 31,35,55,59,77,89.arrow_forwardConsider the following Turing Machine (TM). Does the TM halt if it begins on the empty tape? If it halts, after how many steps? Does the TM halt if it begins on a tape that contains a single letter A followed by blanks? Justify your answer.arrow_forwardPllleasassseee ssiiirrrr soolveee thissssss questionnnnnnnarrow_forward
- 4. def modify_data(x, my_list): X = X + 1 my_list.append(x) print(f"Inside the function: x = {x}, my_list = {my_list}") num = 5 numbers = [1, 2, 3] modify_data(num, numbers) print(f"Outside the function: num = {num}, my_list = {numbers}") Classe Classe that lin Thus, A pro is ref inter Ever dict The The output: Inside the function:? Outside the function:?arrow_forwardpython Tasks 5 • Task 1: Building a Library Management system. Write a Book class and a function to filter books by publication year. • Task 2: Create a Person class with name and age attributes, and calculate the average age of a list of people Task 3: Building a Movie Collection system. Each movie has a title, a genre, and a rating. Write a function to filter movies based on a minimum rating. ⚫ Task 4: Find Young Animals. Create an Animal class with name, species, and age attributes, and track the animals' ages to know which ones are still young. • Task 5(homework): In a store's inventory system, you want to apply discounts to products and filter those with prices above a specified amount. 27/04/1446arrow_forwardOf the five primary components of an information system (hardware, software, data, people, process), which do you think is the most important to the success of a business organization? Part A - Define each primary component of the information system. Part B - Include your perspective on why your selection is most important. Part C - Provide an example from your personal experience to support your answer.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
C++ Programming: From Problem Analysis to Program...Computer ScienceISBN:9781337102087Author:D. S. MalikPublisher:Cengage Learning
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole
C++ Programming: From Problem Analysis to Program...
Computer Science
ISBN:9781337102087
Author:D. S. Malik
Publisher:Cengage Learning