I had asked a question, which can be found here :
And had been suggested Linear programming. I have looked up Linear programming and the Simplex method. But all the examples that I have come across have inequality constraints which are converted into equalities using slack variables. The simplex method then interchanges the basic and the non basic variables to obtain an optimal solution.
But my problem is :
x1 + x2 + ... + xn
subject to :
a1*x1 + a1*x2 + a1*x3 + ... + a1*xn = c1;
a2*x1 + a2*x2 + a2*x3 + ... + a2*xn = c2;
a3*x1 + a3*x2 + a3*x3 + ... + a3*xn = c3;
Now I don't know how I can apply the simplex method here as I don't have any basic variables here.
Also I can't just solve the linear equations as I have n variables and 3 equations.
Can someone suggest me a way out here?