Title
To Build Or Not To Build (Dorothy Gieck)
Goals
Students will work with the concept of probability. Students will work in small groups in order to arrive at a method for deciding whether a company should build a new factory or not. They will be able to organize, explain, and justify how they arrived at this method to the rest of the class.
Abstract
This activity, which is set in the context of the business world, asks students to make a decision for a company on whether to build a new factory or not based on given information. Students are asked to form small groups to discuss the problem and come to a method for finding what they believe to be the best solution to the problem. This activity could be used with a probability unit.
Problem Statement
When faced with uncertainties, mathematical expectations often give us advantages in making decisions. When we need to choose between two or more alternatives, it is considered "rational" or " most promising " to choose the option with the result that leads to maximized expected profits, minimized expected costs, maximized expected tax advantages, minimized expected losses, and so on.
A clothing manufacturer must decide whether to spend a considerable sum of money to build a new factory. He knows that if the new factory is built and the clothing business has a good sales year, there will be a $451,000 profit; if the new factory is built and the clothing business has a poor sales year, there will be a deficit of $110,000; if the new factory is not built and the clothing business has a good sales year, there will be a $220,000 profit (mostly because of lower overhead cost). If the clothing manufacturer feels that the probabilities for a good sales year or a poor sales year are, respectively, 0.40 and 0.60, would building the new factory maximize his expected profit?
Instructor Suggestions
1. Set the stage by discussing the "Problem Statement" (see above) with your students.
2. Distribute the "To Build or not to Build" activity sheet and allow the students to individually read the activity.
3. Discuss the terms profit and deficit, maximizing and minimizing.
4. Have students form small groups to derive an answer to the problem.
5. When the small groups are finished, have a spokesperson for each group share the group answers for specific parts of the activity and explain their method and reasoning involved in arriving at their decision.
6. Discuss the students' work as it relates to probability and real world situations.
Materials
"To Build or not to Build" activity sheet, blackboard and chalk or white board and markers.
Time
Introduction of Problem Statement (5 min.), small group work (25 min.), presentation of small group work and large group discussion (15 min.), extension questions (5 min.)
Mathematics Concepts
Discrete Mathematics Concepts
Counting Techniques, Probability, Markov Chains, Maximizing options, Expectations
Related Mathematics Concepts
Combinations, Permutations, Probability, Profit and Loss
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be adapted to many levels of mathematics. It could be integrated into any class that is studying probability. I would use it to help review or reinforce concepts that had already been introduced with probability. It would relate probability to real world problems and introduce new vocabulary from the business world.
Further Investigation
What if the expectations for a good or poor sales year changes, does this change the decision?
Variations/Comments
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Colorado Model Content Standards for Mathematics (1995)
Freund, J., Simon, G. (1995), Statistics, A First Course. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.