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.
 Linear Program Solver for Simplex Method for Several Variables
 Linear Program Grapher for Two Variable Problems
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: 111
Template for Geometric Linear Programming Problems
Video Examples for Chapter 3
Video: basic example for solving a linear program MAXimum problem using the graphical
method
https://www.youtube.com/watch?v=M4K6HYLHREQ PatrickJMT
Video: basic example for solving a linear program MAXimum problem using the graphical
method
https://www.youtube.com/watch?v=YPn4yHM1YsU Howard Community College
Video: basic example for solving a linear program MINimum problem using the graphical
method
https://www.youtube.com/watch?v=2ACJ9ewUC6U PatrickJMT
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 TI83 and TI84 families of calculators. It can not be downloaded to other models or brands of calculators.
USE TI83+ or TI84+ 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
https://www.youtube.com/watch?v=M5szdUhYxFI Kevin Pinegar
Chapter 4 Homework
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
Do NOT do assignment Part D below. We did minimization by simplex method as a lab instead. You do not need to do the assignment below and that material (Dual Program) is not on the exam.
***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!