Week 4: Linear programming

The week's question: What is he 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 to to get on with other things? This is the question of optimal browsing. Animals have to eat some minimum amount to meet their metabolic requirements for survival. Once those has been met do they 1) continue to eat to maximize their energy intake in order to become bigger, stronger, accumulate more fat for overwintering, or increase their reproductive success, 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 (LP, nothing to do with computer programming), which enable us to find maxmimum and minimum values, and model optimization processes. This week we will learn the 8-step process for solving linear programming problems graphically. The processs is straightforward, but long. It takes 20 to 30 minutes to do a single problem at first. This week's entire exercise set is just two problems!

(Next week we will see how to solve higher dimensioned LP problems by pivoting matrices.)

Take control of your learning

I order the resources for each week in the same sequence I would teach them in a face-to-face class. This doesn't mean you have to read and watch them in this sequence, and having them all at the start of the week opens some new possibilities for you. You can look at the summary notes, before the example problems. Look at the Exercise problems, before reading/watching anything. Feel free to experiment to find what works for you.

One other thing. Some research suggests that instructional videos should be 5-10 minutes long. Some this week's are much longer than that, but you control the pause button, feel free to use it as required.

Exercises vs Assignments

The exercises are like physical exercises: prescribed actions to complete to develop a skill. They typically tell you just 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 or exhaustive seaarch, 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 related to the week's material, but extend the techniques learned, or sometimes point out limitations in those techniques.

If that seems vague here are some implications for Assignment 2. Problem 1 does not require, or even benefit from, using a matrix. Two of the matrices in Problem 4 will have peculiar "solutions". And maybe the spreadsheet you create for Problem 5 could be useful in other problems...

Upcoming survey

The second exercise this week will be to complete a short survey. Teaching in a classroom I can tell what is working and what isn't, and get some feel for how you are finding the course (putting your head down on the desk is a dead give away 😆). Teaching online I can't, so I have to ask. Is there anything *you'd* like to know about your classmates? If you have a question to suggest, send it to me and I'll consider adding it to the survey.

Reminder: Exercise Set 3 is due by 4 pm today!

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

Assignment 2 is due by 4 pm this Friday

Submit PDF files of work done by hand, or in a word processor. (Let me know if you are unsure how to create these.) Email is preferred, but you can also submit your work through Moodle.
Excel spreadsheet files should be sent as file attachments.
Google sheets can be submitted by sharing a link to them.

Name the file you submit A2_firstname.pdf, e.g.

A2_Tim.pdf

If you have to submit multiple files, add a suffix number to each, e.g.

A2_Tim_1.pdf
A2_Tim_2.xls

Office Hours: Get help, or just come by to say "Hi"

I'll have office hours again this week (and every week) on Monday, Wednesday and Friday from 10:30 am to 11:30 am in my Zoom "office". Feel free to stick your head in to say a quick hello, or to stay a while and tell me what you're up to. It's optional, but I look forward to meeting you.

That's all for now!

Stay well and stay in touch,
Tim