Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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
Which tool takes the 2 provided input datasets and produces the following output dataset? Input 1: Record First Last Output: 1 Enzo Cordova Record 2 Maggie Freelund Input 2: Record Frist Last MI ? First 1 Enzo Last MI Cordova [Null] 2 Maggie Freelund [Null] 3 Jason Wayans T. 4 Ruby Landry [Null] 1 Jason Wayans T. 5 Devonn Unger [Null] 2 Ruby Landry [Null] 6 Bradley Freelund [Null] 3 Devonn Unger [Null] 4 Bradley Freelund [Null] OA. Append Fields O B. Union OC. Join OD. Find Replace Clear selection
What are the similarities and differences between massively parallel processing systems and grid computing. with references
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=xsin⁡x 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. 6.3 - 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