1. Chapter 3 Section 4 Linear Programming Algebra 2 January 29, 2009

2. Warm-Ups  Each week you must do a minimum of 18 hours of homework. Participation in sports requires at least 12 hours per week. You have no more than 35 hours per week to devote to these activities  A) Write a system of inequalities to model this situation  B) Graph and solve the system  C) What does the feasible region represent in this problem?

3. Quiz Review!!  An ordinary refrigerator costs $498 and has an estimated cost of $84 per year. An energy-saving model costs $599, with an estimated cost of $61 per year. After how many years will the costs to buy and to operate the models be equal?  You’ll also need to know:  How to solve a system of equations using either substitution or elimination  How to solve a system of inequalities by graphing

4. Vocabulary  Linear Programming: A technique that identifies the minimum or maximum value of some quantity  This quantity is modeled with an objective function.  Limits on the variables in the objective function are constraints  These are written as linear inequalities

5. Testing Vertices  What values of x and y maximize P for the following objective function?

6. Testing Vertices  STEP 1: Graph the constraints  STEP 2: Find the coordinates for each vertex  STEP 3: Evaluate P at each vertex

7.  Use the same constraints from the last problem. Find the values for x and y that maximize and minimize the objective function:

8. Another Example  Find the values of x and y that maximize and minimize P for the following objective function:

9. Need More Examples??  Graph the system of constraints. Name all vertices. Then find the values of x and y that minimizes the objective function.

10. Homework #15 Pg 142 #1-6