Linear Programming

Fellow: Brooke OdleTeacher: Maria Sanchez

School: St. Vincent AcademyJanuary 10, 2012

Objective

• Solve a real-world problem using linear programming– Use graphing calculator to solve problems

A Review

• What is linear programming?• Linear programming is the process of finding

the maximum or minimum of a function for a region defined by inequalities

How is Linear Programming used in the Real World?

• Linear programming is used whenever one is interested in maximizing profit and minimizing costs.

• Fields that use linear programming include:– Business & Management– Telecommunications– Math & Industrial Engineering (Operations Research)– Manufacturing &Transportation– Scheduling

Linear Programming Procedure1. Define the

Variables2. Write a system of

inequalities3. Graph the system

of inequalities

4. Find the coordinates of the

vertices of the feasible region

5. Write a function to be maximized or

minimized

6. Substitute the coordinates of the vertices into the

function

7. Select the greatest or least

result. Answer the problem.

Real-World Problem #1

• Cookie Dough Kit Fundraiser…– Problem adapted from Texas Instruments’

website: Linear Programming Activity

Real-World Problem #2

• Sporting Goods Manufacturer…– Problem obtained from Henrico County Public

Schools (Virginia) website: Algebra 2 Online! webpage• Module: Solving Systems of Linear Equations and

Inequalities • Notes: Linear Programming Sample(pdf)