Week 3
Linear Programmming

⦿ Monday. Linear Programming: First example

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 manufacture to maximize profit?

Summary: Linear programming

Notes summarizing the procedure for solving a linear programming problem graphically.

Terminology: Linear programming

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.

⦿ Wednesday. Linear Programming: Two more examples

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 $2,000US to put a pound of matter into orbit.

⦿ Friday. Linear Programming: The moose case study

Handout: Moose data [PDF]

This 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 energy intake? Which ones 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.