## Linear Programming

### Resources

Linear Program Geometric Solution Template for Chapter 3

#### Linear Programming Lab Chapter 4

We will most likely do a Linear Programming Lab on the computer in a lab (or on iPads in the classroom) one day while working in Chapter 4.  More information will be posted here about the lab, location, worksheet and due date (or in Course Studio in MyPortal) at the appropriate time.

#### Free Online Linear Program Solver

The first link is for simplex method for several variables and second link is for a linear program grapher for two variable problems. You can use these to check your Ch 3 and Ch 4 homework but you will need to know how to do the problems yourself for quizzes and exams.  These are helpful tools but do not replace learning how to do the procedures graphically or on your calculator.

### Chapter 3 Geometric Method

It may be helpful to use a solution sheet template posted online to help remember the steps.  Eventually you need to remember all the steps yourself without a template.

#### Homework Section 3.1

• Do Problems 1, 2, 3, 5, 6

#### Homework Section 3.2

• Do Problems 1, 2, 3, 4

To check the final answers for ALL assigned homework problems in sections 3.1 and 3.2 click HERE.  It will open in a new window or tab.

If you need additional practice in chapter 3, do Chapter Review problems in Section 3.3: 1-11

Template for Geometric Linear Programming Problems

### Chapter 4  Simplex Method

You need Calculator Program APIVOT for Chapter 4 to make simplex method calculation procedures faster and easier.  This program automates all the row operation procedures needed to perform the Simplex Method for Chapter 4. The instructor will download the program to students calculators in class. This program runs only on TI-83 and TI-84 families of calculators.  It can not be downloaded to other models or brands of calculators.

USE TI-83+ or TI-84+ program APIVOT to do the Simplex Method.  Do NOT do your row operations individually for the pivots unless you did not get this program downloaded to your calculator from the instructor.

You are learning a little bit about how computers use procedures called algorithms to solve problems, so that when/if you use a computer to solve a problem like this in the future, its not entirely "magic" to you about how it goes about solving it.

#### Video Example for Section 4.2 Simplex Method (Standard Max): If you want VIDEO help:

Video: basic example for solving a linear program standard maximum problem using the simplex method
Two things are done differently here than in our class
1) he uses the letter s as the symbol for the slack variables but our book and class use the letter y as the symbol for the slack variables
2) he shows the row operations for the pivot step.  In our class we use the calculator program APIVOT to automate the work for these row operations

#### Section 4.1

• READ this section for background about how linear programming is used in the real world.
• There are no homework problems assigned for section 4.1

#### ***Chapter 4: Assignment Part A

Write  these word problems in linear program form, stating whether you are minimizing or maximizing, state the objective function and state all constraints.

Section 4.2 Problems 3, 4, 5
Section 4.4 Review Problems 9 and 10

You will solve the problems above later, for Chapter 4 Assignment Part B using the simplex method.
For Assignment Part A just write the linear program in standard form.

2 Practice Problems to set up Linear Programs with 2 or 3 variables , MIXED Constraints

Will open in a new tab or window as a pdf file.  The solutions are on the second page, to check your answers.
Write  these problems in linear program form, stating whether you are minimizing or maximizing, state the objective function and state all constraints.
Do NOT solve these problems.  (If you really want to solve them use the Linear Program Simplex Tool link near the top of this page to solve using technology.)

#### ***Chapter 4 Assignment Part B

Section 4.2 Simplex Method for Standard Maximum Problems

• Do Problems 1, 3, 4, 5 & Section 4.4 Review Problems 9 and 10
• If you need extra practice:

• Section 4.2 Problem 2 for mechanics
• Section 4.4 Review problems: 1, 2, 3, 4, 5 for mechanics
• Section 4.4 Review problem 10 for application word problems

Its highly recommended to do as many practice word problems as you can!

#### ***Chapter 4  Assignment Part C

Section 4.3  Setting up linear programming models as objective function and constraints

• Section  4.3 #9 and Section 4.4 Review Problem #11 - write each word problem as a mathematical linear programming mode

#### ***Chapter 4 Assignment Part D

Section 4.3  Solving Standard Minimum Problems using the Dual

• Do Problems 1, 2, 3, 4 & Section 4.4 Review Problem 11
• If you need extra practice:
• Section 4.4 Review problems:  6, 7, 8 for mechanics
• Section 4.4 Review problem 12 for application word problems.

Its highly recommended to do as many practice word problems as you can!