Linear Programming Chapter 3

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Questions and Answers

What is the primary reason for using computer solutions in linear programming?

To reduce the use of mathematical methods

To make computations easier and reliable (correct)

To replace human judgment in decision making

To make computations more complex

What is sensitivity analysis used for in linear programming?

To find the optimal solution to a linear programming problem

To develop new linear programming models

To analyze the effects of parameter changes on the optimal solution (correct)

To replace computer solutions with manual calculations

What was the primary method of solving linear programming problems in the 1940s?

Manual calculations

Computer solutions

Sensitivity analysis

The simplex method (correct)

What is one of the primary benefits of using computer solutions in linear programming?

Easier and more reliable computations Signup and view all the answers

Why do managers need to learn quantitative methods in decision making?

To generate greater profitability Signup and view all the answers

What is the purpose of applying sensitivity analysis in linear programming?

To analyze the effects of parameter changes on the model solution Signup and view all the answers

What is the main advantage of using computer solutions in linear programming?

Easier and more efficient computations Signup and view all the answers

What must be checked on the Solver Parameters screen to ensure Solver uses the simplex procedure?

Select a Solving Method as Simplex LP Signup and view all the answers

What appears in column H of the spreadsheet if there are extra resources left over?

Slack Resources Signup and view all the answers

What is the purpose of the Solver Results screen that appears after clicking 'OK'?

To provide a summary of the solution results Signup and view all the answers

What must be in a consistent form before a linear programming model can be solved with QM for Windows?

Constraints Signup and view all the answers

What is the purpose of the 'Solve' button at the bottom of the Solver Parameters screen?

To solve the model and display the solution Signup and view all the answers

Where is the 'Make Unconstrained Variables Non-Negative' option located?

Solver Parameters screen Signup and view all the answers

What type of procedure does Solver use to solve the model if 'Simplex LP' is selected?

Simplex procedure Signup and view all the answers

What is the first step in solving the problem using the Solver?

Click on the ―Data‖ tab on the toolbar Signup and view all the answers

What is the purpose of the ―Set Objective‖ field in the Solver Parameters window?

To input the objective function cell Signup and view all the answers

What is the purpose of the Add Constraint window?

To add the model constraints Signup and view all the answers

What is the alternative way to input the model constraints?

By adding a single constraint formula Signup and view all the answers

Why is it not necessary to input the nonnegativity constraints for the decision variables?

Because it can be done in the Solver Parameters screen Signup and view all the answers

What should you do after adding all the model constraints?

Click on ―OK‖ to return to the Solver Parameters screen Signup and view all the answers

What is the main reason behind the decrease in focus on the simplex method in teaching linear programming?

The availability of personal computers and linear programming software has made it easier to solve linear programming problems. Signup and view all the answers

What is the advantage of using a spreadsheet to solve linear programming problems?

It enables the problem to be set up in an attractive format for reporting and presentation purposes. Signup and view all the answers

What is the main difference between using a spreadsheet and a software package like QM for Windows?

The spreadsheet requires more data input. Signup and view all the answers

What is the advantage of using a spreadsheet as a template for other problems?

It saves time and effort in setting up the problem. Signup and view all the answers

Why is the simplex method not as popular in teaching linear programming as it once was?

The availability of computers and linear programming software has made it easier to solve linear programming problems. Signup and view all the answers

What is the main difference between Excel spreadsheets and software packages like QM for Windows?

Excel spreadsheets require more data input, while software packages require only model parameters. Signup and view all the answers

Study Notes

Linear Programming: Computer Solution and Sensitivity Analysis

Overview

Linear programming has become an essential tool for businesses to make efficient decisions amidst intense competition.
Managers need to learn quantitative methods, including linear programming, to make effective decisions, especially in terms of profitability.
Computer solutions are necessary to make linear programming computations easier and more reliable.

Computer Solution

Linear programming was first developed in the 1940s using the simplex method.
With the evolution of computer technology, linear programming models can now be solved quickly and cheaply using prewritten software packages.
The simplex method has become less of a focus in linear programming teaching due to the easy availability of personal computers and software.

Excel Spreadsheets

Excel can be used to solve linear programming problems, although data input requirements can be time-consuming and tedious.
The advantages of using Excel include setting up a problem in an attractive format for reporting and presentation purposes, and the ability to use a spreadsheet as a template for other problems.

Setting up a Linear Programming Model in Excel

Set up column and row headings for the specific model.
Input constraint and objective function formulas in their entirety.
Use the Solver function in Excel to solve the problem.
Input the objective function cell, decision variables, and model constraints in the Solver Parameters window.
Indicate whether to maximize or minimize the objective function.
Add constraints to the model by clicking "Add" in the Solver Parameters window.
Ensure non-negativity constraints for decision variables are set.

QM for Windows

Constraints must be in a specific form for linear programming models to be solved using QM for Windows.
Variables should appear on the left side of the inequality, and numerical values should be on the right-hand side.

Solving Linear Programming Models

Once the model is set up, click "Solve" to generate the solution.
A Solver Results screen will appear, providing an opportunity to select reports and view the solution.
The answer report provides a summary of the solution results.

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Description

Learn about linear programming methods in business operations, their mathematical approach, and how to make efficient decisions to generate greater profitability.