Minimization linprog constraint no feasible solution

The problem lies in the equality constraints you set up in the code.
In the equality constraints (Aeq and Beq), there are conflicting conditions. Specifically, the last two constraints in Aeq are identical, but they are associated with different values in Beq. This creates a situation where the same set of variables is required to meet two contradictory conditions, making it impossible for linprog to find a feasible solution.
clear;
clc;
%objective cost coefficients
f = [40; 45; 50; 60; 55; 0; 0; 0];

[L1, L2, L3, L4] = deal(2.5, 2, 2, 2.3); %line constraints in per unit
%inequality constraints
Aineq = [0 0 0 0 0 10 -1 0;
0 0 0 0 0 -10 -1 0;
0 0 0 0 0 0 8 0;
0 0 0 0 0 0 -8 0;
0 0 0 0 0 0 0 5;
0 0 0 0 0 0 0 -5;
0 0 0 0 0 0 5 0;
0 0 0 0 0 0 -5 0];
Bineq = [L1; L1; L2; L2; L3; L3; L4; L4];
%equality constraints
Aeq = [1, 1, 1, 1, 1, 0, 0, 0;
0, 0, 0, 0, 0, 0, 10, 8;
0, 0, 0, 0, 0, 0, 15, -5;
0, 0, 0, 0, 0, 0, 0, 0]

Beq = [2.4 3 4 6.6];
%variable bounds
Lb = [0; 0; 0; 0; 0; -pi; -pi; -pi];
Ub = [3.70; 4.60; 3.40; 3.60; 6.50; pi; pi; pi];%call matlab LP solver
[x,feval,exitflag,output,lambda] = linprog(f, Aineq, Bineq, Aeq, Beq, Lb, Ub);
%display results
disp(x);
disp(feval);

[Torsten]

Which question are you responding to ?

[William]

The code is giving me a "No feasible solution found" error. I don't know why.

[William]

• The text above my code is what my Teaching Assistant said to why I am getting that error.

[William]

I changed the equality constraints to

Aeq = [1, 1, 1, 1, 1, 0, 0, 0;

0, 0, 0, 0, 0, 0, 10, 8;

0, 0, 0, 0, 0, 0, 15, -5;

0, 0, 0, 0, 0, 0, 13, -5]

and still get no feasible solution error.

[Torsten]

You can't give three equalities for two unknowns (x7 and x8). This will almost surely result in a contradiction.

You want x7 and x8 to be

[10 8;15 -5]\[3;4]

ans = 2×1

0.2765 0.0294

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but at the same time you want them to take the values

[15 -5;13 -5]\[4;6.6]

ans = 2×1

-1.3000 -4.7000

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Answer 1

[Torsten]

The last equality constraint says that you want 0*x1 + 0*x2 + 0*x3 + 0*x4 + 0*x5 + 0*x6 + 0*x7 + 0*x8 = 6.6, thus 0 = 6.6 ...

x7 and x8 from the equality constraints 2 and 3 give

[10,8;15,-5]\[3;4]

ans = 2×1

0.2765 0.0294

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At the same time, you want from the inequality constraints 3 and 4

-2/8 <= x7 <= 2/8

which is also a contradiction.

[William]

Thank you! That got me to the correct solution!