OPERATIONS RESEARCH >INTERNATIONAL EDITI
4th Edition
ISBN: 9780534423629
Author: WINSTON
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Question
Chapter 5.2, Problem 8P
(a)
Program Plan Intro
- Let us consider on the following Linear
programming ;
- max z=9x1+8x2+5x3+4x4
- Such that
- x1+x4≤200
- x2+x3≤150
- x1+x2+x3≤350
- 2x1+x2+x3+x4≤550
- x1,x2,x3,x4≥0
- The LINDO output for this Linear Programming is given below:
- Max 9x1+8x2+5x3+4x4
- Subject to constraints:
- x1+x4≤200
- x2+x3≤150
- x1+x2+x3≤350
- 2x1+x2+x3+x4≤550
- End
- LP optimum found at step 4
- Objective function value: 3000.000
Variable Value Reduced Cost x1 200.000000 0.000000 x2 150.000000 0.000000 x3 0.000000 3.000000 x4 0.000000 0.000000
- Number of iterations=4
- Ranges in which the basis is unchanged:
Variable Current Coefficient Obj Coefficient ranges allowable increase Allowance Decrease x1 9.000000 7.000000 1.000000 x2 8.000000 Infinity 3.000000 x3 5.000000 3.000000 Infinity x4 4.000000 0.500000 Infinity
Row Current RHS Righthand side ranges allowable increase Allowance decrease 2 200.000000 Infinity 0.000000 3 150.000000 0.000000 0.000000 4 350.000000 Infinity 0.000000 5 550.000000 0.000000 400.000000
- x1+x4≤200
- x2+x3≤150
- x1+x2+x3≤350
- 2x1+x2+x3+x4≤550
- x1,x2,x3,x4≥0
- x1+x4≤200
- x2+x3≤150
- x1+x2+x3≤350
- 2x1+x2+x3+x4≤550
Variable | Value | Reduced Cost |
x1 | 200.000000 | 0.000000 |
x2 | 150.000000 | 0.000000 |
x3 | 0.000000 | 3.000000 |
x4 | 0.000000 | 0.000000 |
Variable | Current Coefficient | Obj Coefficient ranges allowable increase | Allowance Decrease |
x1 | 9.000000 | 7.000000 | 1.000000 |
x2 | 8.000000 | Infinity | 3.000000 |
x3 | 5.000000 | 3.000000 | Infinity |
x4 | 4.000000 | 0.500000 | Infinity |
Row | Current RHS | Righthand side ranges allowable increase | Allowance decrease |
2 | 200.000000 | Infinity | 0.000000 |
3 | 150.000000 | 0.000000 | 0.000000 |
4 | 350.000000 | Infinity | 0.000000 |
5 | 550.000000 | 0.000000 | 400.000000 |
(b)
Explanation of Solution
- Here, three oddities that may occur when the optimal solution found by LINDO is degenerate.
- Oddity 1: In the ranges in which the basis is unchanged, at least one constraint will have a 0. Allowable increase or Allowable decrease.
- This means that for at least one constraint, the dual price can tell us about the new z-value for either an increase or decrease in the right-hand side, but not both.
- To understand Oddity 1, consider the second constraint. Its allowable increase is 0.
- This means that the second constraint’s dual price of 3 cannot be used to determine a new z-value resulting from any increase in the first constraint’s right-hand side.
- Oddity 2: For a non-basic variable to become positive, its objective function coefficient may have to be improved by more than it reduced cost...
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1
Vo V₁
V3
V₂ V₂
2
1
Vo V₁
V3
V₂ V₂
2
Preparing for a test
Chapter 5 Solutions
OPERATIONS RESEARCH >INTERNATIONAL EDITI
Ch. 5.1 - Prob. 1PCh. 5.1 - Prob. 2PCh. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Prob. 5PCh. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5P
Ch. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Prob. 11PCh. 5 - Prob. 1RPCh. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - Prob. 4RPCh. 5 - Prob. 6RPCh. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - Prob. 10RPCh. 5 - Prob. 11RPCh. 5 - Prob. 12RPCh. 5 - Prob. 13RPCh. 5 - Prob. 14RPCh. 5 - Prob. 15RPCh. 5 - Prob. 16RP
Knowledge Booster
Similar questions
- 1 Vo V₁ V3 V₂ V₂ 2arrow_forwardI need help to solve a simple problem using Grover’s algorithm, where the solution is not necessarily known beforehand. The problem is a 2×2 binary sudoku with two rules: • No column may contain the same value twice. • No row may contain the same value twice. Each square in the sudoku is assigned to a variable as follows: We want to design a quantum circuit that outputs a valid solution to this sudoku. While using Grover’s algorithm for this task is not necessarily practical, the goal is to demonstrate how classical decision problems can be converted into oracles for Grover’s algorithm. Turning the Problem into a Circuit To solve this, an oracle needs to be created that helps identify valid solutions. The first step is to construct a classical function within a quantum circuit that checks whether a given state satisfies the sudoku rules. Since we need to check both columns and rows, there are four conditions to verify: v0 ≠ v1 # Check top row v2 ≠ v3 # Check bottom row…arrow_forwardI need help to solve a simple problem using Grover’s algorithm, where the solution is not necessarily known beforehand. The problem is a 2×2 binary sudoku with two rules: • No column may contain the same value twice. • No row may contain the same value twice. Each square in the sudoku is assigned to a variable as follows: We want to design a quantum circuit that outputs a valid solution to this sudoku. While using Grover’s algorithm for this task is not necessarily practical, the goal is to demonstrate how classical decision problems can be converted into oracles for Grover’s algorithm. Turning the Problem into a Circuit To solve this, an oracle needs to be created that helps identify valid solutions. The first step is to construct a classical function within a quantum circuit that checks whether a given state satisfies the sudoku rules. Since we need to check both columns and rows, there are four conditions to verify: v0 ≠ v1 # Check top row v2 ≠ v3 # Check bottom row…arrow_forward
- I need help to solve a simple problem using Grover’s algorithm, where the solution is not necessarily known beforehand. The problem is a 2×2 binary sudoku with two rules: • No column may contain the same value twice. • No row may contain the same value twice. Each square in the sudoku is assigned to a variable as follows: We want to design a quantum circuit that outputs a valid solution to this sudoku. While using Grover’s algorithm for this task is not necessarily practical, the goal is to demonstrate how classical decision problems can be converted into oracles for Grover’s algorithm. Turning the Problem into a Circuit To solve this, an oracle needs to be created that helps identify valid solutions. The first step is to construct a classical function within a quantum circuit that checks whether a given state satisfies the sudoku rules. Since we need to check both columns and rows, there are four conditions to verify: v0 ≠ v1 # Check top row v2 ≠ v3 # Check bottom row…arrow_forwardDon't use ai to answer I will report you answerarrow_forwardYou can use Eclipse later for program verification after submission. 1. Create an abstract Animal class. Then, create a Cat class. Please implement all the methods and inheritance relations in the UML correctly: Animal name: String # Animal (name: String) + getName(): String + setName(name: String): void + toString(): String + makeSound(): void Cat breed : String age: int + Cat(name: String, breed: String, age: int) + getBreed(): String + getAge (): int + toString(): String + makeSound(): void 2. Create a public CatTest class with a main method. In the main method, create one Cat object and print the object using System.out.println(). Then, test makeSound() method. Your printing result must follow the example output: name: Coco, breed: Domestic short-haired, age: 3 Meow Meowarrow_forward
- Q2) by using SHI-Tomasi detector method under the constraints shown in fig. 1 below find the corner that is usful to use in video-steganography? 10.8 ...... V...... 0.7 286 720 ke Fig.1 Threshold graph. The plain test is :Hello Ahmed the key is: 3a 2x5 5b 7c 1J 55 44 2X3 [ ] 2x3arrow_forwardusing r languagearrow_forwardWhat disadvantages are there in implicit dereferencing of pointers, but only in certain contexts?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 ColeC++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology PtrNp Ms Office 365/Excel 2016 I NtermedComputer ScienceISBN:9781337508841Author:CareyPublisher:Cengage

Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole

C++ for Engineers and Scientists
Computer Science
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Course Technology Ptr
Np Ms Office 365/Excel 2016 I Ntermed
Computer Science
ISBN:9781337508841
Author:Carey
Publisher:Cengage