Chapter 3 Section 4
Linear Programming
Algebra 2
January 29, 2009
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?
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
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
Testing Vertices

What values of x and y maximize P for the following
objective function?
Testing Vertices

STEP 1: Graph the constraints

STEP 2: Find the coordinates for each vertex

STEP 3: Evaluate P at each vertex

Use the same constraints from the last problem. Find the
values for x and y that maximize and minimize the
objective function:
Another Example

Find the values of x and y that maximize and minimize
P for the following objective function:
Need More Examples??

Graph the system of constraints. Name all vertices. Then
find the values of x and y that minimizes the objective
function.
Homework #15
Pg 142 #1-6