Feasible Systems

Two things may prevent the existence of a solution. There may be no values of x and y satisfying the constraints. Even if there are such values, there may be none maximizing the objective function. If there are values satisfying the constraints, the system is called feasible.

The following example illustrates a set of inequality constraints with no function to be maximized or minimized. You can ask whether the constraints are feasible—that is, whether they define a nonempty set. Just click the matrix, and from the Simplex submenu choose Feasible.


$\blacktriangleright$ Simplex + Feasible?

4x + 3y≤6
3x + 4y≤4
x≥ 0
y≥ 0
, Is feasible? true

 

4x + 3y≤6
4x + 3y≥7
, Is feasible? false


Saying that the system
4x + 3y≤6
4x + 3y≥7
is not feasible implies, in particular, that there are no values minimizing the objective function in the problem
x + y
4x + 3y≤6
4x + 3y≥7
 .