MIT Massachusetts Institute of Technology

Optimizing Your Diet: What Linear Programming Can Tell You!

Aysegul Topcu
Senior Operations Researcher
Structured Decisions Corporation
West Newton, MA

In this video lesson, students will learn about linear programming (LP) and will solve an LP problem using the graphical method. Its focus is on the famous "Stigler's diet" problem posed by the 1982 Nobel Laureate in economics, George Stigler. Based on his problem, students will formulate their own diet problem and solve it using the graphical method. The prerequisites to this lesson are basic algebra and geometry. The materials needed for the in-class activities include graphing paper and pencil. This lesson can be completed in one class of approximately one hour. If the teacher would like to cover the simplex algorithm by George Dantzig as an alternative solution method, an additional whole class period is suggested.

Aysegul Topcu graduated with a Ph.D. in Industrial Engineering from Northeastern University in 2009. She currently works as a senior operations researcher at the Structured Decisions Corporation in West Newton, MA where she uses operations research methods to develop mathematical models for complex logistical operations in the service industries. She truly enjoys being part of a team that works on problems she never imagined operations research has the answers for!

First article on the diet problem – Stigler’s diet problem George J. Stigler, "The Cost of Subsistence,” Journal of Farm Economics, 27, 1945, pp. 303-14.
http://www.jstor.org/pss/1231810

Dantzig’s diet problem George Dantzig, “The diet problem,” Interfaces 20: 4 July-August 1990, pp 43-47.
http://www.jstor.org/pss/25061369

Diet Problem Solver: This page, sponsored by the Finite Mathematics and Applied Calculus website, can help you solve a diet problem.
http://www.zweigmedia.com/RealWorld/dietProblem/diet.html

Simplex Method Tool – Type your own linear programming problem, and it will give you the solution. The page is sponsored by the Finite Mathematics and Applied Calculus website.
http://www.zweigmedia.com/RealWorld/simplex.html

Sponsored by the Wolfram Demonstrations Project website, this page presents a visualization of a simple standard linear programming scenario.
http://demonstrations.wolfram.com/ASimpleStandardLinearProgrammingScenario/

From the online textbook - Algorithm Animations for Practical Optimization: A Gentle Introduction
http://optlab-server.sce.carleton.ca/POAnimations2007/Default.html

MIT’s OpenCourseWare: Lecture notes on linear programming
http://ocw.mit.edu/courses/mathematics/18-310c-principles-of-applied-mathematics-fall-2007/lecture-notes/26_27_ln.pdf

Introduction to Linear Programming by John Chinneck, a professor at Carleton University in Ottawa, Canada.
http://www.sce.carleton.ca/faculty/chinneck/po/Chapter2.pdf

You're on top of the game.

Anonymous
November 25, 2011 at 6:40 am

You're on top of the game. Thanks for shairng.

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This Lesson is in the following clusters: Computer Programming

You're on top of the game.

Anonymous
November 25, 2011 at 6:40 am

You're on top of the game. Thanks for shairng.