I am interested in ideas what to teach when the task is to teach a bit of (linear) optimization to third year undergraduate mathematics students.
Assume 'a bit' means I'd have about eight hours of lecturing time.
The students know standard linear algebra results and some multivariable real analysis (including basic optimality criteria via derivatives, and also Lagrange multiplier method). They do not know much (or any) numerical mathematics in a narrow sense, but at least in part have some knowledge of programming and algorithms.
An immediate idea is discussing the simplex algorithm. But what else?
I am tangentially familiar with various mathematically interesting subjects around this, but I do not know what could be feasible to discuss. I am also not strictly committed on the idea that it is all about linear optimization.
Answers could include a plan for these lectures or also recommendations for individual subjects that could be feasible to cover in the given context. Pointers to lecture notes in that direction or other relevant literature are welcome as well.