Download Linear Programming Lesson Plan

Lesson Title: Linear Programming
Date: 8/3/2011
Teacher(s): V. Stamper
Course: Algebra 2
Start/end times: _________________________
Lesson Objective(s): What mathematical skills and understanding will be developed?
A.REI.11
Students will solve real-world problems in order to develop an understanding of how to optimize given situations
using linear programming.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific questions, problems, tasks,
investigations, or activities will students be working on during the lesson?
Linear Programming word problems source: http://www.purplemath.com/modules/linprog.htm
In this activity, students will solve real-world optimization problems using linear programming.
1. The teacher will introduce the linear programming task and strategically pair/group students. Each
pair/group will be assigned one of the four problems, graph paper, rulers, color pencils, markers, chart paper,
and a graphing calculator. The students will read the problem to determine how to optimize the given task.
2. Pairs/groups will begin working to complete the task. The teacher will circulate the room to monitor the
students’ progress and ensure that students are on task. The teacher may ask thought provoking questions to
help students that may be struggling with the task.
3. After students have been working for 15 minutes, the teacher will ask students to copy their solutions on the
chart paper to present their solutions to the class.
4. Each pair/group will be asked to present their solution and explain the strategies that were used to complete
the task.
5. With the entire class, the teacher will pose the following questions:
 What is a feasible region?
 What is meant by optimization?
 Is optimization the maximum or minimum?
 What were some of the constraints in the problems?
Evidence of Success: What exactly do I expect students to be able to do at the end of the lesson, and how will I
know? That is, deliberate consideration of what performances will convince you (and any outside observer) that
your students have accomplished your objective.
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Students will be able to determine the unknowns (x and y variables).
Students will be able to write and graph systems of inequalities.
Students will be able identify the feasible region, the constraints, and optimal situation for the task.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
The teacher will present the students with the following
scenario: Easy Electronics Company wants to keep
production costs down. The company produces digital
audio players and digital video players. The following
information was posted by the factory production
manager on the company bulletin board:
Player
Audio
Production per Shift
Minimum Maximum
600
1500
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow?
Teacher will ask students the following questions:
One pair/group will summarize the strategies used to solve
each of the four problems.
Cost per
Unit
$55
HCPSS Secondary Mathematics Office; adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.
Lesson Title: Linear Programming
Date: 8/3/2011
Teacher(s): V. Stamper
Video
800
1700
$95
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Course: Algebra 2
Start/end times: _________________________
How much does it cost to produce 1000 audio
players? $55,000
Is it cheaper to produce an audio player or a
video player? an audio player
Can the company produce 2000 audio players
per shift? Why? No; the maximum number
of audio players that can be produced is
1500.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Vocabulary: constraints, feasible region, linear programming, maximum, minimum, optimize
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Linear Programming Word Problem
Graph paper
Ruler
Color pencils
Markers
Chart Paper
Graphing Calculators
A school is preparing a trip for 400 students. The company who
is providing the transportation has 10 buses of 50 seats each and
8 buses of 40 seats, but only has 9 drivers available. The rental
cost for a large bus is $800 and $600 for the small bus.
Calculate how many buses of each type should be used for the
trip for the least possible cost.
a. Identify the unknowns.
b. Write a system of inequalities to represent the situation.
c. Draw the graph showing the feasible region.
d. List the coordinates of the vertices of the feasible
region.
e. Determine the number of each type of bus.
f. What is the minimum cost?
Post Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use
to reflect on the effectiveness of this lesson?
Were the students able to accomplish the task?
What were the students’ stumbling blocks?
Does the lesson need to be modified?
Did the lesson meet my expectations?
HCPSS Secondary Mathematics Office; adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.