Define optimal solution in a linear programming problem

An optimal solution to a linear programming problem is the solution that satisfies all the constraints while achieving the maximum or minimum value of the objective function.

To simplify, in a linear programming problem, we are given:

• An objective function, which we need to either maximize or minimize.
• A set of constraints that define the feasible region.

After applying these constraints, we get a feasible region, which is the set of all possible solutions that satisfy the constraints. The optimal solution is found by evaluating the extreme points of this region and selecting the one that gives the highest or lowest value of the objective function.

Note:

Every linear programming problem has an extreme point that provides an optimal solution. However, it is not always guaranteed that we can easily identify it.