MaplePrimes - answers and comments on Question, linear programming

ok thank you. Does there

alex_01 — Sun, 02 May 2010 22:41:14 Z

ok thank you. Does there exist any alternative methods ?
I read something about introducing an auxiliary variable

hirnyk — Sun, 02 May 2010 22:42:15 Z

It is well known that this problem can be reduced to the following problem of linear programming:

maximize f=x1+x2+x3

under the constraints

3*x1+2*x2+3*x3<=1, x1+4*x2+6*x3<=1, 3*x1+5*x2+x3<=1, xj>=0,j=1..3.

Here is its solution by Maple 13:

> with(simplex):

> maximize(x1+x2+x3,{3*x1+2*x2+3*x3<=1,x1+4*x2+6*x3<=1,3*x1+5*x2+x3<=1},NONNEGATIVE);.

The output is {x1=13/65,x2=4/65,x3=6/65}, the probability p1=x1/(x1+x2+x3)=0.56522.

hirnyk — Sun, 02 May 2010 23:15:43 Z

In fact, x1,x2, and x3 are auxiliary variables.

I also tried to solve the irreduced problem by Optimization, but unsuccessfully.

Here is an attempt:

> with(Optimization):

> NLPSolve( min(E1, E2, E3),

{E1 = 3*p1 + p2 + 3*p3, E2 = 2*p1 + 4*p2 + 5*p3,E3 = 3*p1 + 6*p2 + 1*p3,

p1+p2+p3=1,p1<=1,p2<=1,p3<=1}, assume = nonnegative,maximize);

Error, (in Optimization:-NLPSolve) unable to compare -E3+E2 and 0)