OPERATIONS RESEARCH >INTERNATIONAL EDITI
OPERATIONS RESEARCH >INTERNATIONAL EDITI
4th Edition
ISBN: 9780534423629
Author: WINSTON
Publisher: CENGAGE L
bartleby

Concept explainers

Question
Book Icon
Chapter 6, Problem 34RP
Program Plan Intro

Optimal solution:

  • Consider the linear programming problem given below:
  • max z= 20x1+10x2
  • Subject to constraints:
    • x1+x2=150
    • x140
    • x220
    • x1,x20
  • Here,
  • xi= Fraction of investment I purchased by star oil.
  • The Lindo output of the LP is given in the following figure:
  • LP optimum found at step 5
  • Objective function value: 57.44902.
VariableValueReduced Cost
x11.0000000.000000
x20.2008600.000000
x31.0000000.000000
x41.0000000.000000
x50.2880840.000000
RowSlack or SurplusDual prices
10.0000000.190418
20.0000000.984644
30.0000007.951474
40.7991400.000000
50.00000010.124693
60.00000012.063268
70.7119160.000000
  • Number of iterations: 5
  • Ranges in which the basis is unchanged:
Obj coefficient ranges
VariableCurrent coefficientAllowable increaseAllowable Decrease
x113.000000Infinity7.951474
x216.00000045.1045279.117647
x316.000000Infinity10.124693
x414.000000Infinity12.063268
x539.00000051.66666830.245285
Right-hand side ranges
RowCurrent RHSAllowable increaseAllowable Decrease
140.00000038.2647069.617647
220.00000011.2758638.849056
31.0000001.1393731.000000
41.000000Infinity0.799140
51.0000001.9957451.000000
61.0000002.3191491.000000
71.000000Infinity0.711916

Explanation of Solution

b.

  • The given LP is called the primal. If the primal is a max problem, then the dual will be min problem. Define the variables for the max problem to be z,x1,x2,...........,xn and the variables for the min problem to be w,y1,y2,........,yn.
  • max z= c1x1+c2x2+.......+cnxn
  • subject to constraints
    • a11x1+a12x2+.......+a1nxnb1
    • a21x1+a22x2+.......+a2nxnb2
    • am1x1+am2x2+.......+amnxnbm
  • The dual of the normal max problem is defined below:
  • min w=b1y1+b2y2+.......+b2yn
  • subject to constraints
    • a11y1+a12y2+.......+a1nync1
    • a21y1+a22y2+.......+a2nync2
    • am1y1+am2y2+.......+amnyncm
  • Given a max problem, the primal is read across the table and the dual is found by reading down.
min w (x10)(x20)

max z

(xn0) 
  x1x2 xn 
(y10)y1a11a12a1nb1
(y20)y2a21a22a2nb2
 
(ym0)ymam1am2amnbm
  c1c2 cn 
  • The given problem is a non normal Max problem

Blurred answer
Students have asked these similar questions
The images I have uploaded are the part 1 to 4 and questions below are continue on the questions uploaded 5. C++ Class Template with Method Stubs #pragma once #include <iostream> #include <string> #include <stdexcept> #include <vector>   template <typename T> class HashTable { private:     struct Entry {         std::string key;         T value;         bool isOccupied;         bool isDeleted;         Entry() : key(""), value(), isOccupied(false), isDeleted(false) {}     };       Entry* table;     size_t capacity;     size_t size;     double loadFactorThreshold;           size_t customHash(const std::string& key) const {         size_t hash = 5381;         for (char c : key) {             hash = ((hash  <<  5) + hash)  +  c;         }         return hash;     }       size_t probe(const std::string& key, bool forInsert = false) const;     void resize();   public:     // Constructor     HashTable(size_t initialCapacity = 101);         // Big…
this project is NOT for graded(marks) purposes, please help me with the introduction. give me answers for the project. i will include an image explaining everything about the project.
Java Graphics (Bonus In this lab, we'll be practicing what we learned about GUIs, and Mouse events. You will need to implement the following: A GUI with a drawing panel. We can click in this panel, and you will capture those clicks as a Point (see java.awt.Point) in a PointCollection class (you need to build this). The points need to be represented by circles. Below the drawing panel, you will need 5 buttons: O о о ○ An input button to register your mouse to the drawing panel. A show button to paint the points in your collection on the drawing panel. A button to shift all the points to the left by 50 pixels. The x position of the points is not allowed to go below zero. Another button to shift all the points to the right 50 pixels. " The x position of the points cannot go further than the You can implement this GUI in any way you choose. I suggest using the BorderLayout for a panel containing the buttons, and a GridLayout to hold the drawing panel and button panels. Regardless of how…

Chapter 6 Solutions

OPERATIONS RESEARCH >INTERNATIONAL EDITI

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
Background pattern image
Computer Science
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole