Linear Programming Code Not Working

A problem which I am working on is shown below.

At this point in time, I have been attempting to solve the problem using the linprog command. I have written out to the best of my ability what I believe Aeq, beq, A, b, and c are, but I am getting an undesireable output. The output states:

Exiting: One or more of the residuals, duality gap, or total relative error has grown 100000 times greater than its minimum value so far:

the primal appears to be infeasible (and the dual unbounded).

(The dual residual < OptimalityTolerance=1.00e-08.)

Any help on fixing this issue would be greatly appreciated. I am not entirely sure that my matrices are all correct, but I believe they are.

xlp = linprog(c, A, b, Aeq, beq, lb, ub);

[Walter Roberson]

please do not close question that have an answer

[Anusha Sridharan]

[Answers Dev] Restored Edits

[Richard McDonough]

i need this question repmved as i posted my code for a class and people were copying it. please let me delete it. your answers did not help me to solve the problem as i already finished the class.

[Walter Roberson]

You can tell your TA or professor that you believe that you may have been copied. Let them handle the situation.

[Walter Roberson]

Richard:

Mathworks Answers is not a private consulting service. The "price" we volunteers charge is that if a volunteer has given a meaningful contribution towards solving the Question, then unless the Question violates policy, then the Question has to stay open so that everyone can learn from the Question and response. No private benefit for the volunteer answers.

If other people are copying your material then you can report that to your TA or professor or your university Office of Academic Integrity.

Answer 1

[Alan Weiss]

I believe that this problem would be much easier to formulate using the problem-based approach rather than the solver-based approach you chose.

But to comment on the problem as you set it up. Many rows in your A matrix have only one entry. You should not have any such rows; they represent bounds, and you should not have them in the A matrix as well.

I am not sure what your control variables represent, so cannot comment further on your setup.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[John D'Errico]

Just to expand on Alan's answer, if we eliminate the redundant constraints, we would recognize that the first 8 unknowns MUST lie between 0 and 10. The second set of 8 unknowns must lie between -5 and 5.

But not only that, since the rest of the constraints actually form cumulative sums of unknowns 9 through 16, and since those cumulative sums are more tightly constrained that the original bounds, we see a set of bounds that looks like:

lb = [zeros(8,1); 0.2; -5*ones(7,1)];
ub = [10*ones(8,1); 0.8; 5*ones(7,1)];

The difference is because that first member of the cumulative sum is now severely limited. So A becomes fairly simple now.

A = [0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0;
     0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0;
     0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0;
     0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0;
     0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0;
     0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0;
     0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1;
     0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0;
     0 0 0 0 0 0 0 0 -1 -1 -1 0 0 0 0 0;
     0 0 0 0 0 0 0 0 -1 -1 -1 -1 0 0 0 0;
     0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 0 0 0;
     0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 0 0;
     0 0 0 0 0 0 0 0 -1  -1 -1 -1 -1 -1 -1 0;
     0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1];

b = [repmat(0.8,7,1);repmat(0.2,7,1)];
c = [4 3 2 3 7 6 5 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8]';

[X,FVAL,EXITFLAG] = linprog(c,A,b,Aeq,beq,lb,ub)

No feasible solution found.

Linprog stopped because no point satisfies the constraints.

X =
     []
FVAL =
     []
EXITFLAG =
    -2

I'd bet you can show that the equality constraints are inconsistent with that set of bounds and linear inequalities.