Feasible and Optimal Solutions

A solution (values for the decision variables) for which all of the constraints in the Solver model are satisfied is called a feasible solution. The Solver proceeds by first finding a feasible solution, and then seeking to improve upon it, changing the decision variables to move from one feasible solution to another feasible solution until the objective function has reached its maximum or minimum. This is called an optimal solution.

How does the Solver know (more important, how do you know) that the solution is optimal? The answer to this question depends on the type of problem (linear/quadratic, nonlinear or integer) you are trying to solve, which is discussed at some length in the next section.