Week 3: Linear programming


Photo by Zachery Perry on Unsplash

The week's question: What is that moose↑ up to?

This week's material is built around answering a question about the handsome fellow above: When he gets back to browsing, will he be trying to eat as much as he can, or will he eat as quickly as he can so he can get on with other things? This is the question of optimal foraging. Animals have to eat some minimum amount to meet their metabolic requirements for survival, but once those needs have been met, what do they do? Do they:

  1. Continue to eat to maximize their energy intake in order to become bigger, stronger, and accumulate more fat for overwintering, or to increase their reproductive success,

    2. or do they,

  2. Try to minimize the time they spend eating to reduce their predation risk, maintain thermal balance, and spend more time selecting a mate and caring for offspring?

Linear programming

To help us answer this question we will explore the tools of Linear Programming (abbreviation: LP; nothing to do with computer programming). These tools will enable us to find maximum and minimum values, and to model optimization processes. This week we will learn the procedure for solving linear programming problems graphically. The process is straightforward, but looong (8 steps! 🫠). At first it can take 20 to 30 minutes to do a single problem, and this week's entire exercise set is just two problems!

(Next week we will see how to solve LP problems with more than two dimensions by...pivoting matrices!)

Exercises vs Assignments

You have probably noticed that the exercises and assignments are quite different. The exercises are like physical exercises: prescribed actions to complete to develop a skill. 💪 They typically specify how to complete a problem, e.g. "Use a matrix to..." Assignments are different, with an "anything goes" ethos. In the first week we saw that there are multiple ways to solve any problem: visually by drawing, numerically by trial and error, exhaustive search, algebraically by symbol manipulation, and intuitively through insight. On assignments you are encouraged to use any and all techniques that move you towards a solution.

Assignment questions are also integrative, they are based on the week's material, but often combine the techniques learned that week or extend them (and sometimes point out limitations in those techniques). 🤯

If that seems vague here are some implications for Assignment 2. Maybe the spreadsheet you created for Exercise Set 2.3 could be helpful to you. Two of the matrices in Problem 4 will have peculiar "solutions". And problem 5 does not require, or even benefit from, using a matrix.

Reminder: Exercise Set 2 is due by the start of class Monday!

Be sure to hand me, or send me, your work. Don't let these easy marks slip through your fingers.

Assignment 2 is due by 1 pm this Friday

You can hand me a paper copy of your work or email me digital files.

If you send me digital files, name them A2_firstname.suffix, e.g. I might use:

A2-Tim.pdf
A2-Tim.xls

to send a PDF of a scan and a spreadsheet.

"Office" Hours: Get help, or just stick around to say "Hi"

As a sessional instructor I don't have an office in the building, but I'm happy to stay after class and answer any questions you might have, provide just-in-time review of a topic, or just chat.

That's all for now!

See you soon,
Tim