tag:blogger.com,1999:blog-8231784566931768362.post2933130904769031237..comments2021-06-16T05:56:38.112-04:00Comments on MathNotations: Santa Knows Linear Programming!Dave Marainhttp://www.blogger.com/profile/13321770881353644307noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8231784566931768362.post-74553149578144658022008-12-18T20:55:00.000-05:002008-12-18T20:55:00.000-05:00Thanks Eric and Happy Holidays!I really think all ...Thanks Eric and Happy Holidays!<BR/><BR/>I really think all hs math students who plan on continuing their study should see the parametric argument to which you're referring. It's instructive and elegant and I guess I should consider developing this as an investigation or a video.<BR/><BR/>As far as giving students a view of real-world applications of LP, I see it both ways. Show them an application, a video perhaps, showing professionals who utilize the technique. This provides some motivation and an overview. One needn't worry over the complexity of this professional application - it's just giving the 'big picture.' A careful incremental development can then follow. Many lessons often gloss over the practical application and focus only on the procedure.<BR/><BR/>By the way, I am willing to bet that Santa's problem will provide formidable to many students even if they have had an introduction to LP. Keeping track of even a small number of variables and setting up those constraints can be mind-boggling for many youngsters.Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-399479974804393312008-12-18T19:43:00.000-05:002008-12-18T19:43:00.000-05:00The important technique to get from this simple pr...The important technique to get from this simple problem (remembering that practical LP problems are much worse) is that the answer must lie at a vertex of the problem domain. It's a fun thing to show, and doesn't require any calculation at all; just a simple argument on parametric equations for line segments.<BR/><BR/>Finding the vertices shouldn't be a difficult task either.<BR/><BR/>However, you may have problems explaining how LP problems occur in real life; the difference between a toy problem like this and the problem of supplying the Sixth Fleet with food and ammunition with the least transport cost is a few orders of magnitude.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-44090804240907418592008-12-18T19:08:00.000-05:002008-12-18T19:08:00.000-05:00Happy Holidays, Sean, to you and your students!I w...Happy Holidays, Sean, to you and your students!<BR/>I would be interested in their reactions, how many will attempt this, never mind solve it. <BR/><BR/>They may need a calculator for some of the computation. Would you also give them graph paper for more accurate graphing (as opposed to a quick sketch)? <BR/><BR/>This 'extra credit' problem will be time consuming so you may also consider giving this as an extra credit problem outside of class (mention an honor system there but expect some collaboration!). Another possibility is, for that half day before the holidays (if you get one), have them compete against each in teams of 2,3, or 4.<BR/><BR/>Thanks for your support as always...Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-90732688203877161152008-12-18T13:25:00.000-05:002008-12-18T13:25:00.000-05:00Well, since my trig class went over this exact thi...Well, since my trig class went over this exact thing earlier this semester, I put it in as an extra credit question. We'll se if they like it.Sean Hendersonhttps://www.blogger.com/profile/00996947122054737906noreply@blogger.com