In linear programming, a basic solution is a solution that satisfies all of the constraints of the problem and is expressed in terms of a set of basic variables. A basic variable is a variable that is associated with one of the constraints in the problem and takes on a non-zero value in the solution.
An optimal solution, on the other hand, is a solution that is the best possible among all the feasible solutions to the problem. In other words, it is the solution that maximizes or minimizes the objective function (also known as the decision function), subject to the constraints of the problem.
In general, a linear programming problem can have multiple basic solutions, but only one of these solutions will be optimal. The process of solving a linear programming problem involves finding the optimal solution by identifying the values of the variables that maximize or minimize the objective function while satisfying all of the constraints of the problem.
