Week 4
Linear Programmming
Business
Review topics
Optional. Just in time review. Just in case you've forgotten.😉
Review: Calculating percentage error. This previously appeared in the Discussion Forum, but to make it more visible I'm placing it here too.
Review: Dividing fractions.
Linear Programming
- Example: Sleds and Toboggans 📹 Pencast 34:26|📘 PDF
- We begin with a simplified production problem: If we have some available resources in the form of time and material what should we make to maximize profit?
- Summary: Linear programming 📄 Weg page
- Notes summarizing the procedure for solving a linear programming problem graphically.
- Terminology: Linear programming 📄 Weg page
- A glossary of terms I may use in the pencasts, exercises and assignment this week. Let me know if I missed any, and I'll add them.
- Example: Furniture manufacturing 📹 Pencast 24:28|📘 PDF
- Another manufacturing problem, this time with three production stages, so we end up with three constraints. Otherwise quite similar to the sleds and toboggans example.
- Example: NASA nutrition 📹 Pencast 22:22|📘 PDF
- Linear progamming isn't only about factories and manufacturing.Here is a simplified nutritional problem, where the goal is to minimize the weight of food required to meet nutritional needs. This is important because it costs approximately $10,000US to put a pound of matter into orbit.
- Handout: Moose data 📘 PDF
- Here is most of the data we need to determine whether moose are maximizing energy or minimizing time. Take a look at the labels and values in the table to familiarize yourself with the problem. Which values are relevant to enery intake? Whichones to time taken?
There is an additional constraint that is not contained in the table: moose require sodium, which they can only get from aquatic macrophytes. The average moose needs 2.57g of sodium per day, and the density of sodium in the aquatic plants they eat is 0.003g/g.
- Case Study: Moose foraging behaviour 📹 Pencast 38:09|📘 PDF
- Finally we have the tools to answer the question: Are foraging moose maximizing their energy intake, or minimizing their time spent foraging?
Our strategy will be to use linear programming to figure out how moose would behave if they were 1) maximizing, or 2) minimizing, and then to look at observational data to see which one their behaviour is closest to.
All models are wrong
- All models are wrong 📄 Slide Show
- They are. Really. But that's not the whole story...
Supplementary resources
Some of you have requested traditional textbook-like materials for the course content. Here are some for the Simplex method for maximization (unfortunately they use a different approach than we do for minimization).
- Linear programming - A geometric approach Chapter 3 from Applied Finite Mathematics by Sekhon and Bloom.
- Sections 3.1-3.3 in Module 3 ofFinite Mathematics from Lumen Learning. Though note that unlike almost everyone else in the world they shade in the feasible set rather than shading outside it.
If you would like an interactive tutorial see Solving linear programming problems graphically. If the text is very small (as it was for me) remember that you can ahve your browser scale it up by pressing Ctrl-+ or Command-+ repeatedly.
If you use any of these resources, please let me know how you found them! Even a simple 0-3 star rating would be helpful.
Exercise Set
Exercise Set 4 Part 1: Problems and Solutions. Due by 4 pm Monday February 1.
Exercise Set 4 Part 2: A brief feedback survey. (Also linked from the Moodle home page in case this link doesn't work.) To be completed by 4 pm Monday February 1.
Assignment
Assignment 3. Due by 4 pm Friday February 5.