Hello Jennifer,
Are you certain that our problems are worrectly written?
For intstance, why is there a "2" alone in a line of the first problem ?
And why do your right-hand side elements all have "x" ("0x", "1x", "15x")?
I cannot rewrite them but I can tell you that yes, karmarkar allows to
solve such problems.
Just have a look at its help page :
http://help.scilab.org/docs/5.4.1/fr_FR/karmarkar.html
Your first problem should look something like this:
c = [1 -2 0 0 4]'; // Main problem
Aeq = [1 0 -1 0 0 ; ? ? ? ? ? ; 1 -2 4 0 -4 ; ? 2 0 1 -4 ; ? 1 1 1 1];
// Equations
beq = [0 ? 0 0 1]; // Right-hand side
[xopt, fopt, exitflag, iter, yopt] = karmarkar(Aeq, beq, c)
If the solution is not all positive (inequality constraint), add an
inequality matrix A, like in the help page.
Hope that helps,
Paul.
On 10/10/2013 05:38 AM, Jennifer Basbas wrote:
Dear All,
I am new to Scilab and I'm wondering if anyone can help me solve the
following minimization problem in linear programming using Scilab:
1. Apply Karmarkar's algorithm to solve
Minimize -
x1 - 2x2 + 4x5subject to
x2 - x3 = 0
2
x1 - 2x2 + 4x3 - 4x5 = 0x
1 + 2x2 + x4 - 4x5 = 0x
1 + x2 + x3 + x4 + x5 = 1x
1, x2, x3, x4, x5 >= 0
2. Apply the primal affne scaling algorithm to solve
Minimize -
2x1 + x2subject to
x1 - x2 + x3 = 15x
2 + x4 = 15x
1, x2, x3, x4 >= 0
Hint: The optimal solution is
x* = [30 15 0 0]T with optimal value -45.
Any inputs will be greatly appreciated. Thank you.
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