Guided Notes: Linear Programming
Name:_________________________
Activity: Finding Minimum Value
Suppose you wanted to buy some mp3s and some CDs. You can afford as many as 10 mp3s or 7 CDs.
You want at least 4 CDs and at least 10 hours of recorded music. Each tape holds about 45 minutes of
music, and each CD hold about an hour.
1. Write a system of inequalities to model the problem.
X=
Y=
2. Graph the system.
New Vocabulary:
1. Linear Programming –
2. Objective Function –
3. Constraints –
Questions:
1. What is the objective function from our activity problem? What are the constraints?
Guided Notes: Linear Programming
Name:_________________________
Graphing:
When we graph our linear program we come up with a: _____________________ the part of our graph
that ____________________ all the _________________ that satisfy all the _____________________.
Vertex Principal:
If there is a _____________________ or _________________________ value of the linear objective
function it occurs at one or more ________________________ of the __________________________.
Example:
Given the following constraints what values of x and y maximize P form the objective function
P = 3x+2y?
3
𝑦 ≥ 2𝑥 −3
Constraints = 𝑦 ≤ −𝑥 + 7
𝑥≥0
{ 𝑦≥0 }
Step 1: Graph the Constraints:
-
Using our calculator
Step 2: Find the Coordinates of each vertex (where the lines intersect):
-
Using our calculators
Step 3: Evaluate P at each vertex:
-
Plug in coordinates to see which one gives us the bigger number:
Guided Notes: Linear Programming
Name:_________________________
Word Problem:
Suppose you are selling cases of mixed nuts and roasted peanuts. You can order no more than a total of
500 cans and packages and spend no more than $600. There are 12 cans per case and 20 packages per
case. How can you maximize your profit? How much is the maximum profit.
Steps to solve:
-
Step 1: Define our variables:
X=
Y=
P=
-
Step 2: Make a table of our information:
-
Step 3: Write and Simplify Constraints
-
Step 4: Solve
o Graph constraints
o Find the coordinates of each vertex
o Evaluate P at each vertex