2. LINEAR PROGRAMMING
Linear Programming is a method for
finding a minimum or maximum value
of some quantity, given a set of
constraints
Constraints are restrictions on the
variables of the objective function in a
linear programming problem.
The constraints form a system of
inequalities
The graph of the system is the feasible
region, it contains all the points that
satisfy all the constraints
The objective function is a model
(equation) of the quantity that you want
to make as large or as small as
possible.
3. VERTEX PRINCIPLE OF LINEAR
PROGRAMMING
If there is a maximum or minimum value of the
linear objective function, it occurs at one or more
vertices of the feasible region.
To find the maximum or minimum
1. Graph the constraints to form the feasible region
2. Find the coordinates of each vertex
(Solve the system – for the two equations that intersect at that
vertex – using the method of your choice)
3. Evaluate the objective function using each vertex to
find the maximum or minimum
6. EXAMPLE – PAGE 159
You are screen printing T-shirts and sweatshirts to sell at
the Polk County Blues Festival and are working with the
following constraints
You have at most 20 hours to make shirts
You want to spend no more than $600 on supplies
You want to have at least 50 items to sell
How many T-shirts
and how many
sweatshirts should
you make to
maximize your
profit?What is the
maximum profit?
7. EXAMPLE
1. Organize the information in a table
T-Shirts Sweatshirts Total
2. Write the constraints and objective function
3. Solve and Answer the question
