@mmcdara 

Sorry for the download file problem. I was having trouble with Maple losing connection to the server all morning. Thanks again.

@acer Your answer is going to make an interesting weekend. A lot to digest. Thanks again.

@acer 

You are so right, thanks again.

The results from time() function are not correct. I did stop watch experiments and obtain 60s with Threads and 90s with no Threads. So there are improvements with using Threads. 

I had a feeling orthopoly:-P() may be a problem, but also int() and W(). Thanks for taking time to answer my question.

@Axel Vogt Thanks alot, I spent more than an hour trying solve this problem.

@Lilian 

By adding the statement infolevel[Optimization] = 1 to your calculations, you will find that the methods used by LSSolve on list_1 were modifiednewton and sqp. This may account for the unexpected results. I tried forcing the run with constraints to use modifiednewton and it blew up. LSSolve knows better than me.

May I add one more comment on the use of intitialpoints, which you will find in the Help on LSSolve under the Notes section: "It is recommended that you try different initial points with each problem to verify that the solution is indeed an extremum."

worksheet_help_GL.mw 

RecordSomething_2.mw

Hi, I found that you do not need the DocumentToolsin part for it to work.