# EXCEL SOLVER TUTORIAL

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

## Transcription

1 ENGR62/MS&E111 Autumn Prof. Ben Van Roy October 1, 2003 EXCEL SOLVER TUTORIAL This tutorial will introduce you to some essential features of Excel and its plug-in, Solver, that we will be using throughout ENGR62 to solve linear programs (LPs). You will learn how to represent LPs in an Excel worksheet, use the matrix functions SUMPRODUCT and MMULT, set up an LP in Solver, and generate various outputs from Solver. This quarter you will see many applications of Solver in class demonstrations and homework assignments. Keep this tutorial document as a reference as you review the class demos and as you formulate LPs in your homeworks. For additional Excel/Solver assistance, try consulting the Excel Help files or numerous online resources. Parts of this tutorial borrow from Prof. Veinott s detailed Formulating and Solving Linear Programs in Excel. 1 Setting Up Linear Programs In Excel Linear programs (LPs) can take many forms. In ENGR62 we will often be dealing with LPs that can be represented mathematically as maximize c T x subject to Ax b, where the matrices A, b, and c comprise the problem data. Our goal is to maximize the value of the objective function, c T x, by choosing an appropriate vector of decision variables, x. The matrices A and b specify a set of linear inequality constraints that reflect the requirements of the problem.

2 EXCEL SOLVER TUTORIAL Page 2 of 6 a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 a 41 a 42 a 43 a 51 a 52 a 53 Each matrix element occupies a cell in the worksheet. Entering Matrices into Excel It is easy to display the components of an LP in their natural way in Excel, i.e., as a range of cells. For example, if A is a 5 3 matrix, then each element of A can be entered into its corresponding cell in a 5 3 range of cells. Identify ranges of cells to contain the data matrices A, b, and c and enter them into the Excel worksheet. Do the same for the decision variables, x. To keep your worksheet organized, you might consider arranging the matrices as shown below. You are also encouraged to use labels and text to document your work. c T c T x A x Ax b A sample layout of LP matrices in an Excel worksheet. Naming Matrices in Excel Excel allows you to name ranges of cells in the worksheet. This feature is especially convenient for doing matrix calculations and for setting up LPs in Solver. To name a range of cells, select the entire range with the mouse and use the Insert Name Define... menu. Alternatively, select the range and enter its name in the Name Box adjacent to the Formula Bar. Try using both methods to give names to the data matrices A, b, and c and to the decision variables, x.

3 EXCEL SOLVER TUTORIAL Page 3 of 6 Matrix Calculations: SUMPRODUCT and MMULT We will frequently use the SUMPRODUCT and MMULT commands in Excel. Syntax SUMPRODUCT(range1, range2 ) MMULT(range1, range2 ) Description sum of products of corresponding elements ordinary matrix multiplication The arguments of SUMPRODUCT and MMULT can be either ranges of cells or range names. It is more concise and descriptive to use names. For a pair of ranges named S and T, entering SUMPRODUCT(S,T) into the Formula Bar returns i,j s ijt ij, i.e., the sum of the products of corresponding elements of S and T. Entering MMULT(S,T) into the Formula Bar returns the matrix whose ij th element is k s ikt kj, i.e., normal matrix multiplication. SUMPRODUCT(S,T) will return an error unless S and T have the same dimensions. Similarly, MMULT(S,T) will return an error unless the number of columns of S equals the number of rows of T. If you need to take the transpose of a matrix, use the TRANSPOSE function. Important note: If a matrix function returns a matrix larger a single element, you must first use the mouse to select the cells that will contain the result, then type the matrix function into the Formula Bar, and finally type CTRL SHIFT ENTER (COMMAND ENTER on a Mac) to evaluate the matrix function. For example, if S and T are 3 5 and 5 4 matrices, respectively, then the result of MMULT(S,T) will be a 3 4 matrix. To perform this calculation and display the result in the worksheet, first highlight a 3 4 range of cells, type MMULT(S,T) into the Formula Bar, then type CTRL SHIFT ENTER to display the result in the highlighted area. With regard to LPs, two of the most important matrix calculations are computing the objective function value, c T x, and the constraint function, Ax. The objective function value c T x is the scalar product of two vectors, and so can be computed using either SUMPRODUCT(c,x) (as long as c and x are both either row or column vectors) or MMULT(cT,x. 1 The constraint function Ax is a matrix, so MMULT(A,x) must be used. Select ranges of cells to contain c T x and Ax and compute their values using the Excel matrix functions. As the following section will make clear, it is helpful to give these ranges names such as ctx or OF for c T x, and Ax for Ax. Also remember that neither SUMPRODUCT nor MMULT will work properly if either of the two arguments are empty. For this reason, you must provide dummy values such as zeros for the decision variables, x. 1 The MMULT command shown here assumes that the objective function coefficients, c, have been entered as a row matrix and named ct. Of course, how you issue matrix function commands in Excel will depend on how you entered the data into your worksheet. If you entered c as a column, then you would compute c T x as MMULT(TRANSPOSE(c),x).

4 EXCEL SOLVER TUTORIAL Page 4 of 6 2 Using Solver Setting up the LP in Solver When all of the LP components have been entered into the worksheet and given names, bring up Solver using the Tools Solver... menu. There are four main elements of the Solver dialog box: Set Target Cell: The Target Cell contains the quantity you wish to optimize the objective function value. To specify the Target Cell, either click on the cell with the mouse or type in the name of the cell containing the objective function value (e.g., OF or ctx). Equal To: This specifies the direction of the optimization. Max or Min radio buttons. Click on either of the By Changing Cells: Recall that our goal is to optimize the value of the objective function by choosing an appropriate vector of decision variables. Therefore we will allow Excel to change the decision variables, x. In the By Changing Cells: field, either select the range of decision variables using the mouse or type in the name of the range (e.g., x). Subject to the Constraints: Specify a constraint by clicking on the Add button. While it is possible to add each constraint one at a time, it is easier (and more concise) to enter a single inequality between the constraint function, Ax, and the right-hand side, b. If Ax and b are named ranges in the worksheet, enter the constraint as Ax b. 2 Be sure to include any additional constraints, such as nonnegativity constraints (x 0). On the right hand side of the Solver dialog box is a button labeled Options... Click on this button to bring up another dialog box. Since we will be dealing primarily with linear programs in ENGR62, the option of greatest interest is Assume Linear Model. Selecting this option forces Excel to use a method for solving LPs known as the Simplex algorithm, which we will discuss in some detail later in the course. It is important that Assume Linear Model is selected, or else you may end up with inappropriate outputs. Once the LP has been properly set up in the Solver dialog box, press the Solve button to run Solver. 2 Or whatever the appropriate inequality is. You may find it easier to separate,, and = constraints into blocks, provide appropriate names, then enter them into Solver.

5 EXCEL SOLVER TUTORIAL Page 5 of 6 Solver Output Options Pressing the Solve button runs Solver. Depending on the size of the LP, it may take some time for Solver to get ready. If Solver reaches a solution, a new dialog box will appear and prompt you to either accept the solution or restore the original worksheet values. At this point you may also choose to see a number of output reports. The Answer report provides a summary of the optimal decision variable values, binding and non-binding constraints, and the optimal objective function value. The Sensitivity report provides information describing the sensitivity of the optimal solution to perturbations in the problem data. This report will become important during our study of linear programming duality. A Note About What to Hand In Solving an LP in Excel can sometimes take up a lot of worksheet space, especially if there are many variables or constraints. Although it is important for you to set up your worksheets correctly and neatly, it is not necessary unless clearly stated by the assignment for you to submit them with your homework. Instead, you may print out and submit the Answer and Sensitivity reports that accompany your Solver solution. 3 An Example Consider the following linear program: max 50x x x x 4 subject to 2x x 2 + 3x x x 1 + 1x 2 + 2x x x x x x x 2 50 x 3 30 x 1, x 2, x 3, x 4 0 This problem can easily be represented as an LP of the form maximize subject to c T x Ax b x 0,

6 EXCEL SOLVER TUTORIAL Page 6 of 6 where data matrices A, b and c T are A = , b = , ct = [ ] Note that two of the inequality constraints have been reversed to become constraints. In an Excel worksheet, identify ranges of cells to accommodate A, b, c T, and x, and name the ranges appropriately. In this example we will assume these ranges have been named A, b, ct, and x, respectively. Initialize the vector of decision variables x with some dummy values such as zeros. Select a position for the objective function, define it using the function MMULT(cT,x), and name it ctx, say. Similarly, define the constraint function Ax using MMULT(A,x) and name the result Ax. 3 Open Solver from the Tools Solver... menu. Enter the following information into the dialog box: Set Target Cell: ctx Equal to: check Max radio button By Changing Cells: x Subject to the Constraints: Ax b and x 0 Before pressing Solve, make sure that Assume Linear Model has been checked in the Options... dialog box. Then press Solve. Generate Answer and Sensitivity reports, and examine your solution. For another example of how to set up a linear program in Excel/Solver, download the telecommunications example (teleco.xls) from the course website. Observe how ranges are named, and how the names are used in the Solver window. 3 Remember that since Ax is a 5 1 matrix, you will first have to highlight a 5 1 range of cells and press CTRL SHIFT ENTER to evaluate MMULT(A,x).

### SUPPLEMENT TO CHAPTER

SUPPLEMENT TO CHAPTER 6 Linear Programming SUPPLEMENT OUTLINE Introduction and Linear Programming Model, 2 Graphical Solution Method, 5 Computer Solutions, 14 Sensitivity Analysis, 17 Key Terms, 22 Solved

### Using Excel to Find Numerical Solutions to LP's

Using Excel to Find Numerical Solutions to LP's by Anil Arya and Richard A. Young This handout sketches how to solve a linear programming problem using Excel. Suppose you wish to solve the following LP:

### Matrix Operations Using Mathcad Charles Nippert

Matrix Operations Using Mathcad Charles Nippert These notes describe how to use Mathcad to perform matrix operations. As an example you'll be able to solve a series of simultaneous linear equations using

### How to create graphs with a best fit line in Excel

How to create graphs with a best fit line in Excel In this manual, we will use two examples: y = x, a linear graph; and y = x 2, a non-linear graph. The y-values were specifically chosen to be inexact

### Using EXCEL Solver October, 2000

Using EXCEL Solver October, 2000 2 The Solver option in EXCEL may be used to solve linear and nonlinear optimization problems. Integer restrictions may be placed on the decision variables. Solver may be

### Linear Programming. March 14, 2014

Linear Programming March 1, 01 Parts of this introduction to linear programming were adapted from Chapter 9 of Introduction to Algorithms, Second Edition, by Cormen, Leiserson, Rivest and Stein [1]. 1

### USING EXCEL 2010 TO SOLVE LINEAR PROGRAMMING PROBLEMS MTH 125 Chapter 4

ONE-TIME ONLY SET UP INSTRUCTIONS Begin by verifying that the computer you are using has the Solver Add-In enabled. Click on Data in the menu across the top of the window. On the far right side, you should

### max cx s.t. Ax c where the matrix A, cost vector c and right hand side b are given and x is a vector of variables. For this example we have x

Linear Programming Linear programming refers to problems stated as maximization or minimization of a linear function subject to constraints that are linear equalities and inequalities. Although the study

### problem is to maximize 2x1 +4x2 +3x3 + x4 subject to: 3x1 + x2 + x3 + 4x4» 12 x1 3x2 + 2x3 + 3x4» 7 2x1 + x2 + 3x3 x4» 10 x 0 : I set up the sample te

Linear Programming Notes IV: Solving Linear Programming Problems Using Excel 1 Introduction Software that solves moderately large linear programming problems is readily available. You can find programs

### Tutorial: Using Excel for Linear Optimization Problems

Tutorial: Using Excel for Linear Optimization Problems Part 1: Organize Your Information There are three categories of information needed for solving an optimization problem in Excel: an Objective Function,

### Mathematical Programming

1 The Add-in constructs models that can be solved using the Solver Add-in or one of the solution add-ins provided in the collection. When the Math Programming add-in is installed, several new command lines

### Linear Programming Notes V Problem Transformations

Linear Programming Notes V Problem Transformations 1 Introduction Any linear programming problem can be rewritten in either of two standard forms. In the first form, the objective is to maximize, the material

### Notes on Excel Forecasting Tools. Data Table, Scenario Manager, Goal Seek, & Solver

Notes on Excel Forecasting Tools Data Table, Scenario Manager, Goal Seek, & Solver 2001-2002 1 Contents Overview...1 Data Table Scenario Manager Goal Seek Solver Examples Data Table...2 Scenario Manager...8

### Excel supplement: Chapter 7 Matrix and vector algebra

Excel supplement: Chapter 7 atrix and vector algebra any models in economics lead to large systems of linear equations. These problems are particularly suited for computers. The main purpose of this chapter

### Definition of a Linear Program

Definition of a Linear Program Definition: A function f(x 1, x,..., x n ) of x 1, x,..., x n is a linear function if and only if for some set of constants c 1, c,..., c n, f(x 1, x,..., x n ) = c 1 x 1

### Notes on Excel 2007 Forecasting Tools. Data Table Scenario Manager Goal Seek Solver

Notes on Excel 2007 Forecasting Tools Data Table Scenario Manager Goal Seek Solver Paula Ecklund Fall 2008 Contents Page Tools Introduction... 1 Data Table Scenario Manager Goal Seek Solver The Sample

### Linear Programming: Using the Excel Solver

Outline: Linear Programming: Using the Excel Solver We will use Microsoft Excel Solver to solve the four LP examples discussed in last class. 1. The Product Mix Example The Outdoor Furniture Corporation

### Excel Lab. Figure 1.1: Adding two numbers together in Excel

Excel Lab This document serves as an introduction to Microsoft Excel. Example 1: Excel is very useful for performing arithmetic operations. Suppose we want to add 2 + 3. We begin by entering the number

### Linear Programming. Solving LP Models Using MS Excel, 18

SUPPLEMENT TO CHAPTER SIX Linear Programming SUPPLEMENT OUTLINE Introduction, 2 Linear Programming Models, 2 Model Formulation, 4 Graphical Linear Programming, 5 Outline of Graphical Procedure, 5 Plotting

### Using Formulas & Worksheet Protection in Excel

Common Formulas and Functions Using Formulas & Worksheet Protection in Excel A Formula is sequence of values, cell references, names, functions, or operators in a cell that produces a new value from existing

### Calc Guide Chapter 9 Data Analysis

Calc Guide Chapter 9 Data Analysis Using Scenarios, Goal Seek, Solver, others Copyright This document is Copyright 2007 2011 by its contributors as listed below. You may distribute it and/or modify it

### Microsoft Office Excel 2007 and Spreadsheet Modeling David R. Anderson, Dennis J. Sweeney, Thomas A. Williams and Kipp Martin

89859_01_Excel_Primer.qxd 1/29/08 10:21 AM Page 1 Microsoft Office Excel 2007 and Spreadsheet Modeling David R. Anderson, Dennis J. Sweeney, Thomas A. Williams and Kipp Martin Microsoft Office Excel 2007

### Graphing Parabolas With Microsoft Excel

Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

### Charts in Excel 2007

Charts in Excel 2007 Contents Introduction Charts in Excel 2007...1 Part 1: Generating a Basic Chart...1 Part 2: Adding Another Data Series...4 Part 3: Other Handy Options...6 Introduction Charts in Excel

### Section Notes 4. Duality, Sensitivity, Dual Simplex, Complementary Slackness. Applied Math 121. Week of February 28, 2011

Section Notes 4 Duality, Sensitivity, Dual Simplex, Complementary Slackness Applied Math 121 Week of February 28, 2011 Goals for the week understand the relationship between primal and dual programs. know

### Solving Linear Programs in Excel

Notes for AGEC 622 Bruce McCarl Regents Professor of Agricultural Economics Texas A&M University Thanks to Michael Lau for his efforts to prepare the earlier copies of this. 1 http://ageco.tamu.edu/faculty/mccarl/622class/

### Mathematical finance and linear programming (optimization)

Mathematical finance and linear programming (optimization) Geir Dahl September 15, 2009 1 Introduction The purpose of this short note is to explain how linear programming (LP) (=linear optimization) may

### Excel 2007 Basic knowledge

Ribbon menu The Ribbon menu system with tabs for various Excel commands. This Ribbon system replaces the traditional menus used with Excel 2003. Above the Ribbon in the upper-left corner is the Microsoft

### Macros: Programming Excel/VBA Part II (A.Fring)

Macros: In Labsession 11 you have already seen how to write a subroutine (Macro) using the VBA editor. (not UDF) Alternatively you can also create them with the Macro recorder. In this way you do not need

### Sensitivity Report in Excel

The Answer Report contains the original guess for the solution and the final value of the solution as well as the objective function values for the original guess and final value. The report also indicates

### Formatting. Font formatting. Font formatting options The font formatting options are located on the Home tab within the Font group.

Formatting Font formatting Font formatting options The font formatting options are located on the Home tab within the Font group. Font type Open a workbook called Font formatting. Select the range C3:G3.

### Excel Tutorial 6. Managing Multiple Worksheets and Workbooks COMPREHENSIVE

Excel Tutorial 6 Managing Multiple Worksheets and Workbooks COMPREHENSIVE Objectives Format and edit multiple worksheets at once Create cell references to other worksheets Consolidate information from

### Microsoft Excel 2013 Pivot Tables (Level 3)

IT Training Microsoft Excel 2013 Pivot Tables (Level 3) Contents Introduction... 1 Creating a Pivot Table... 1 A One-Dimensional Table... 2 A Two-Dimensional Table... 4 A Three-Dimensional Table... 5 Hiding

### Exercise 1. Jacek Wiślicki, Laurent Babout,

MS Excel is an example of a spreadsheet, a branch of software meant for performing different kinds of calculations, numeric data analysis and presentation, statistical operations and forecasts. The main

### 1 Solving LPs: The Simplex Algorithm of George Dantzig

Solving LPs: The Simplex Algorithm of George Dantzig. Simplex Pivoting: Dictionary Format We illustrate a general solution procedure, called the simplex algorithm, by implementing it on a very simple example.

### Excel Basics By Tom Peters & Laura Spielman

Excel Basics By Tom Peters & Laura Spielman What is Excel? Microsoft Excel is a software program with spreadsheet format enabling the user to organize raw data, make tables and charts, graph and model

### chapter 1-3 Processing Data using MS EXCEL Introduction Data Entry

chapter 1-3 Processing Data using MS EXCEL Introduction The purpose of this chapter is to highlight those MS EXCEL skills that will be used in the data manipulations used in this text. Those skills include:

### Intermediate Excel 2007

Intermediate Excel 2007 Relative & Absolute Referencing Relative Referencing When you copy a formula to another cell, Excel automatically adjusts the cell reference to refer to different cells relative

### Excel Lab 3: Linear Regression

Excel Lab 3: Linear Regression When working with data sets, the term regression (also called least squares fitting ) refers to determining the formula of a function that relates the data quantities in

### Excel Tips Excel Review Excel

Excel Tips Excel Review Excel 97 1999-2000 Excel Design & Auditing Tips Spreadsheet models are a natural tool for managers but they can be hard to understand and use if they're not well constructed. This

### Microsoft Excel 2003

Microsoft Excel 2003 Data Analysis Larry F. Vint, Ph.D lvint@niu.edu 815-753-8053 Technical Advisory Group Customer Support Services Northern Illinois University 120 Swen Parson Hall DeKalb, IL 60115 Copyright

### Microsoft Excel 2010

Microsoft Excel 2010 An Introduction to MS Excel 2010 STM Training Program Center for Teaching and Learning Prepared by: Niranjan Khadka (Instructional Design Assistant) 1 MS Excel 2010 Formulas and Formatting

### Typical Linear Equation Set and Corresponding Matrices

EWE: Engineering With Excel Larsen Page 1 4. Matrix Operations in Excel. Matrix Manipulations: Vectors, Matrices, and Arrays. How Excel Handles Matrix Math. Basic Matrix Operations. Solving Systems of

### Lecture 5 - Triangular Factorizations & Operation Counts

LU Factorization Lecture 5 - Triangular Factorizations & Operation Counts We have seen that the process of GE essentially factors a matrix A into LU Now we want to see how this factorization allows us

### Pivot Tables How to Series by LACA 3/29/2016

Pivot Tables How to Series by LACA 3/29/2016 Pivot Tables With PivotTable reports, we can look at information in different ways with just a few mouse clicks. Data swings into place, answering questions,

### What is Microsoft Excel?

What is Microsoft Excel? Microsoft Excel is a member of the spreadsheet family of software. Spreadsheets allow you to keep track of data, create charts based from data, and perform complex calculations.

### Creating efficient frontiers using excel.

Creating efficient frontiers using excel. Suppose we have 3 risky assets whose net return has the mean vector and variancecovariance matrix given below: Asset Mean Variance- Covariance Matrix Weights Ones

### Using MS Excel to Analyze Data: A Tutorial

Using MS Excel to Analyze Data: A Tutorial Various data analysis tools are available and some of them are free. Because using data to improve assessment and instruction primarily involves descriptive and

### Stanford University CS261: Optimization Handout 6 Luca Trevisan January 20, In which we introduce the theory of duality in linear programming.

Stanford University CS261: Optimization Handout 6 Luca Trevisan January 20, 2011 Lecture 6 In which we introduce the theory of duality in linear programming 1 The Dual of Linear Program Suppose that we

### Using Excel Pivot Tables. Overview

SacVault Reporting Using Excel Pivot Tables Contact Us: web www.csus.edu/irt/acs/services/cms/training/reference.stm phone (916) 278-7337 Help Desk Last updated 4/15/2009 Overview A Pivot Table is a tool

### Tutorial on Using Excel Solver to Analyze Spin-Lattice Relaxation Time Data

Tutorial on Using Excel Solver to Analyze Spin-Lattice Relaxation Time Data In the measurement of the Spin-Lattice Relaxation time T 1, a 180 o pulse is followed after a delay time of t with a 90 o pulse,

### Linear Programming Models: Graphical and Computer Methods

Linear Programming Models: Graphical and Computer Methods Learning Objectives Students will be able to: 1. Understand the basic assumptions and properties of linear programming (LP). 2. Graphically solve

### Microsoft Excel 2007. Introduction to Microsoft Excel 2007

Microsoft Excel 2007 Introduction to Microsoft Excel 2007 Excel is an electronic spreadsheet to organize your data into rows and columns. One can use it to perform basic to advanced level mathematical

### An introduction to using Microsoft Excel for quantitative data analysis

Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing

### Microsoft Excel 2013 Step-by-Step Exercises: PivotTables and PivotCharts: Exercise 1

Microsoft Excel 2013 Step-by-Step Exercises: PivotTables and PivotCharts: Exercise 1 In this exercise you will learn how to: Create a new PivotTable Add fields to a PivotTable Format and rename PivotTable

### Using Formulas, Functions, and Data Analysis Tools Excel 2010 Tutorial

Using Formulas, Functions, and Data Analysis Tools Excel 2010 Tutorial Excel file for use with this tutorial Tutor1Data.xlsx File Location http://faculty.ung.edu/kmelton/data/tutor1data.xlsx Introduction:

### Excel Worksheet Basics

NDUS Training and Documentation Excel Worksheet Basics Welcome Since Excel has been identified as the spreadsheet application supported by the PeopleSoft system, it s a good idea to learn how to use it

### Excel Modeling Practice. The Svelte Glove Problem Step-by-Step With Instructions

Excel Modeling Practice The Svelte Glove Problem Step-by-Step With Instructions EXCEL REVIEW 2001-2002 Contents Page Number Overview...1 Features...1 The Svelte Glove Problem...1 Outputs...2 Approaching

### Beginner s Matlab Tutorial

Christopher Lum lum@u.washington.edu Introduction Beginner s Matlab Tutorial This document is designed to act as a tutorial for an individual who has had no prior experience with Matlab. For any questions

### Microsoft Excel Tutorial

Microsoft Excel Tutorial Contents Starting MS Excel... 2 The MS Excel Window... 3 Title Bar...3 Office Button...4 Saving Your Work... 4 For the first time... 4 While you work... 4 Backing up your work...

### Linear Programming. April 12, 2005

Linear Programming April 1, 005 Parts of this were adapted from Chapter 9 of i Introduction to Algorithms (Second Edition) /i by Cormen, Leiserson, Rivest and Stein. 1 What is linear programming? The first

### Excel. Design & Audit Tips. Excel Review

Excel Design & Audit Tips Excel Review Spreadsheet models are a natural tool for managers but they can be hard to create from scratch and hard to understand and use if they're not well constructed. This

### Department of Chemical Engineering ChE-101: Approaches to Chemical Engineering Problem Solving MATLAB Tutorial VI

Department of Chemical Engineering ChE-101: Approaches to Chemical Engineering Problem Solving MATLAB Tutorial VI Solving a System of Linear Algebraic Equations (last updated 5/19/05 by GGB) Objectives:

### Math 407A: Linear Optimization

Math 407A: Linear Optimization Lecture 4: LP Standard Form 1 1 Author: James Burke, University of Washington LPs in Standard Form Minimization maximization Linear equations to linear inequalities Lower

### 1. Setting up a small sample model to be solved by LINDO. 5. How do solve LP with Unrestricted variables (i.e. non-standard form)?

Contents: 1. Setting up a small sample model to be solved by LINDO 2. How to prepare the model to be solved by LINDO? 3. How to Enter the (input) Model to LINDO [Windows]? 4. How do I Print my work or

### Quiz 1 Sample Questions IE406 Introduction to Mathematical Programming Dr. Ralphs

Quiz 1 Sample Questions IE406 Introduction to Mathematical Programming Dr. Ralphs These questions are from previous years and should you give you some idea of what to expect on Quiz 1. 1. Consider the

### Q&As: Microsoft Excel 2013: Chapter 2

Q&As: Microsoft Excel 2013: Chapter 2 In Step 5, why did the date that was entered change from 4/5/10 to 4/5/2010? When Excel recognizes that you entered a date in mm/dd/yy format, it automatically formats

### What is Linear Programming?

Chapter 1 What is Linear Programming? An optimization problem usually has three essential ingredients: a variable vector x consisting of a set of unknowns to be determined, an objective function of x to

### Converting a Linear Program to Standard Form

Converting a Linear Program to Standard Form Hi, welcome to a tutorial on converting an LP to Standard Form. We hope that you enjoy it and find it useful. Amit, an MIT Beaver Mita, an MIT Beaver 2 Linear

### CHAPTER 17. Linear Programming: Simplex Method

CHAPTER 17 Linear Programming: Simplex Method CONTENTS 17.1 AN ALGEBRAIC OVERVIEW OF THE SIMPLEX METHOD Algebraic Properties of the Simplex Method Determining a Basic Solution Basic Feasible Solution 17.2

### Linear Programming: Basic Concepts

Linear Programming: Basic Concepts Table of Contents Three Classic Applications of LP The Wyndor Glass Company Product Mix Problem Formulating the Wyndor Problem on a Spreadsheet The Algebraic Model for

### IEOR 4404 Homework #2 Intro OR: Deterministic Models February 14, 2011 Prof. Jay Sethuraman Page 1 of 5. Homework #2

IEOR 4404 Homework # Intro OR: Deterministic Models February 14, 011 Prof. Jay Sethuraman Page 1 of 5 Homework #.1 (a) What is the optimal solution of this problem? Let us consider that x 1, x and x 3

MS Excel Handout: Level 2 elearning Department 2016 Page 1 of 11 Contents Excel Environment:... 3 To create a new blank workbook:...3 To insert text:...4 Cell addresses:...4 To save the workbook:... 5

### A short OPL tutorial

A short OPL tutorial Truls Flatberg January 17, 2009 1 Introduction This note is a short tutorial to the modeling language OPL. The tutorial is by no means complete with regard to all features of OPL.

### value is determined is called constraints. It can be either a linear equation or inequality.

Contents 1. Index 2. Introduction 3. Syntax 4. Explanation of Simplex Algorithm Index Objective function the function to be maximized or minimized is called objective function. E.g. max z = 2x + 3y Constraints

### QC5000 Exporting Results and (SPC) Statistical Process Control

QC5000 Exporting Results and (SPC) Statistical Process Control 1 Exporting, Printing, and Outputting From the file menu, select either Export, Print., or Output. from the image map below. Exporting QC5000

Page 0 German University in Cairo Media Engineering and Technology Prof. Dr. Slim Abdennadher Introduction to Computer Science, Winter 2015 Microsoft Excel 2013 1 Spreadsheet Processing 1.1 Spreadsheet

### Outline. Linear Programming (LP): Simplex Search. Simplex: An Extreme-Point Search Algorithm. Basic Solutions

Outline Linear Programming (LP): Simplex Search Benoît Chachuat McMaster University Department of Chemical Engineering ChE 4G03: Optimization in Chemical Engineering 1 Basic Solutions

### Excel Creating & Using PivotTables. IT Training & Development (818) Information Technology

Information Technology Excel 2007 Users Guide Excel 2007 Creating & Using PivotTables IT Training & Development (818) 677-1700 training@csun.edu www.csun.edu/it/training Table of Contents Introduction...

### Microsoft EXCEL Training Level 3

Microsoft EXCEL Training Level 3 Introduction This tutorial covers creating and using a pivot table to extract different information from one data sample. This course will give you the skills to use a

### Creating Simple Tables and Charts using Microsoft Excel 2013

2015 Bow Valley College 1 Microsoft Excel Vocabulary Creating Simple Tables and Charts using Microsoft Excel 2013 Column: A grouping of information or data organized from top to bottom. In Excel columns

### Figure 1: Excel s data grid and addressing

This is meant to be a short tutorial in how to effectively use Microsoft Excel, a software package that most people are generally familiar with, to plot and analyze scientific data. Basic Excel: First

Operators Lecture 2 Mathcad Basics + Addition, - Subtraction, * Multiplication, / Division, ^ Power ( ) Specify evaluation order Order of Operations ( ) ^ highest level, first priority * / next priority

### Chapter 11. Pivot table

Chapter 11 Pivot table Your worksheet has lots of data, but do you know what the numbers mean? Does your data answer all your questions? PivotTable reports can help to analyze numerical data and answer

### Jeffrey Kantor. August 28, 2006

Mosel August 28, 2006 Announcements Mosel Enrollment and Registration - Last Day for Class Change is August 30th. Homework set 1 was handed out today. A copy is available on the course web page http://jkantor.blogspot.com

### 4.6 Linear Programming duality

4.6 Linear Programming duality To any minimization (maximization) LP we can associate a closely related maximization (minimization) LP. Different spaces and objective functions but in general same optimal

### 1. Data Table. 1.1 The One-Variable Data Table

1. Data Table Data Tables are a tool used frequently in Excel models to track how small changes in inputs affect the results of formulas in your model that are dependent on those inputs. An analysis of

### Matlab Tutorial: Basics

Matlab Tutorial: Basics Topics: 1. Downloading Matlab 2. Opening Matlab 3. Entering Data 4. The Command Window 5. m-files 6. Running m-files 7. Add directory to path 8. Getting help with Matlab functions

TABLE OF CONTENTS CREATING A DATA FILE FOR MAIL MERGE... 3 MAIL MERGE... 3 DATA SOURCE:... 3 FIELD NAMES... 3 Creating the Mail Merge... 3 To create a data file in Excel:... 4 SORTING YOUR DATA IN AN EXCEL

### SPREADSHEET BASIC. A spreadsheet consists of cells arranged in rows and columns. Each cell

1 SPREADSHEET BASIC Basic layout A spreadsheet consists of cells arranged in rows and columns. Each cell can hold text, a number, or a mathematical formula. A cell is referred to by column and row, e.g.,

### Microsoft Excel 2013 Part 2: Intermediate Excel

CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES Microsoft Excel 2013 Part 2: Intermediate Excel Fall 2014, Version 1.0 Table of Contents Introduction...3 Working with Rows and

### Chapter 6. Linear Programming: The Simplex Method. Introduction to the Big M Method. Section 4 Maximization and Minimization with Problem Constraints

Chapter 6 Linear Programming: The Simplex Method Introduction to the Big M Method In this section, we will present a generalized version of the simplex method that t will solve both maximization i and

### Excel -- Creating Charts

Excel -- Creating Charts The saying goes, A picture is worth a thousand words, and so true. Professional looking charts give visual enhancement to your statistics, fiscal reports or presentation. Excel

### Worksheets: Part 2. Class Length: 2 Hours. Objectives:

Worksheets: Part 2 Class Description: This class is an introductory course to the worksheet program, Microsoft Excel. You will learn how to create, edit, and format worksheets. The class will also look

### Computer Training Centre University College Cork. Excel 2013 Pivot Tables

Computer Training Centre University College Cork Excel 2013 Pivot Tables Table of Contents Pivot Tables... 1 Changing the Value Field Settings... 2 Refreshing the Data... 3 Refresh Data when opening a

### above the Ribbon. It contains commands such as Save, Undo, Repeat, Redo and other commands that formerly appeared under drop-down menus.

Beginning Excel 2010 Objective 1: Review Screen Layout Excel 2010 offers the same user interface as 2007. The top portion of the window has a new structure for Excel commands. The band area is called the

### Formulas & Functions in Microsoft Excel

Formulas & Functions in Microsoft Excel Theresa A Scott, MS Biostatistician III Department of Biostatistics Vanderbilt University theresa.scott@vanderbilt.edu Table of Contents 1 Introduction 1 1.1 Using