In linear programming, a feasible solution and an optimal solution differ in how they are defined and how they fit within the issue. Any solution that falls into the feasible region established by the constraints and satisfies all of the restrictions placed on the decision variables is considered feasible. It does not, however, always maximize or minimize the goal function. On the other hand, an optimal solution is a particular workable solution that, depending on the problem's aim, produces the best value for the objective function, either the maximum or the lowest. Because only optimum solutions offer the most advantageous outcomes in terms of the objective function, all feasible solutions are not always optimal even though all optimal solutions are.

An optimal solution, on the other hand, is the feasible solution that yields the best possible value for the objective function, whether it's maximizing or minimizing that function. In summary, all optimal solutions are feasible, but not all feasible solutions are optimal

A feasible solution satisfies all the problem's constraints. An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). A graphical solution method can be used to solve a linear program with two variables.