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Question: Diagnosing '"No Solutions"

Question:Diagnosing '"No Solutions"

ctomkins 156 Maple
October 26 2007
0
I am solving a constrained maximization problem using the Lagrangian and getting back an empty set of solutions, i.e.: solns_LSW:= How do I go about diagnosing why Maple is having difficulty finding solutions? (Once I know that, I would of course also like to know how, if possible, to change the set-up so that Maple might actually find the solution(s)!) I can see that the Lagrangian becomes non-concave for cases where lambda2>p (p is one of the variables I am solving for: there are two, s and p -- see attached worksheet). This would clearly be the case for, say, p=0 optimal (which I have reason to believe it is, based on some numerical simulations I ran). In fact, in the attached worksheet I plot the function I am maximizing and it looks as if the optimal solution is s=m and p=0, but Maple doesn't seem to find this. Thanks! Link to worksheet 'Example-Lagrangian:' http://maplenet.maplesoft.com/maplenet/worksheet/mapleprimes/5475_Example-Lagrangian.mw
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