Lesson 3.4 Linear Programming.notebook
November 02, 2011
3.4 ­ Linear Programming
Objectives
• Be able to find maximum and minimum values of a system of inequalities
• Be able to solve real­world situations using linear programming
Linear Programming:
A technique for finding the
maximum and minimum values of a system of inequalitites
Objective Function:
Feasible Region:
Used to determine the solution
to a linear programing question
The area of all the possible
solutions.
Constraints:
Restrictions placed on the
variables
≤, ≥, <, >
at most
at least
equal to
maximum
minimum
no more than
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Lesson 3.4 Linear Programming.notebook
Variables
Step 1
Graph the constraints
Constraints
Step 2
Find the coordinates of each vertex of the feasible region
November 02, 2011
Objective
Step 3
Evaluate the objective function at each vertex to find the max or min
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Lesson 3.4 Linear Programming.notebook
{
November 02, 2011
12x + 20y ≤ 500
24x +15y ≤ 600
x ≥ 0
y ≥ 0
Maximize P = 18x + 15y
Maximize P = 18x + 15y
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Lesson 3.4 Linear Programming.notebook
November 02, 2011
A furniture manufacturer can make from 30 to 60 tables a day and
from 40 to 100 chairs a day. It can make at most 120 units in one
day. The profit on a table is $150, and the profit on a chair is $65.
How many talbes and chairs should they make per day to maximize
profit? How much is the maximum profit?
Variables
Constraints
Objective
Maximize P = 150x + 65y
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Lesson 3.4 Linear Programming.notebook
November 02, 2011
Maximize P = 150x + 65y
Homework #21
Linear Programming Worksheet
and
Pg. 142 #1-3, 14-16
Chapter 3 Test
MONDAY and FRIDAY!
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Lesson 3.4 Linear Programming.notebook
November 02, 2011
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