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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)