1. Linear Programming Fellow: Brooke Odle Teacher: Maria Sanchez School: St. Vincent Academy January 10, 2012

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

3. 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

4. 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

5. Linear Programming Procedure 1. Define the Variables 2. Write a system of inequalities 3. 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.

6. Real-World Problem #1 Cookie Dough Kit Fundraiser… – Problem adapted from Texas Instruments’ website: Linear Programming ActivityLinear Programming Activity

12. 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)