I've just started learning linear programming, and for some reason, have run into a question about something that isn't mentioned in the first chapter (and we're supposed to answer these questions based on the first chapter).
What is a "basic" solution? It is only mentioned once (so far) in the book, in the following manner:
$$\text{"The solutions we obtain by setting the nonbasic variables to zero are called basic feasible solutions"}$$
But the question now asks; "indicate EACH basic solution, and determine which are feasible and which are infeasible", and I don't see how the above quote says anything about several basic solutions. Surely there's only one way we can set all variables to zero, and so only one basic solution?
For example, what are the basic solutions for something as simple as; $$max \ 2x + y \\ s.t. x + y \le 3 \\ x \le 2 $$ where both variables are nonnegative.
$\endgroup$ 31 Answer
$\begingroup$Rewrite the inequalities as
$$x+y+a=3\\x+b=2\\x\geq0,y\geq0,a\geq0,b\geq0$$
A basic solution has any two of $a,b,x,y$ equal to zero. The other two variables are forced by the two equations.
The feasible basic solutions have the other two variables positive or zero.
