Define the concept of objective function in linear programming.

The objective function in linear programming is a mathematical expression that represents the goal of the problem.

In linear programming, the objective function is used to determine the optimal solution to a problem. It is a linear equation that represents the quantity to be maximised or minimised. The objective function is usually written in terms of decision variables, which are the variables that can be adjusted to achieve the desired outcome. For example, if the objective is to maximise profit, the objective function would be written in terms of the profit variable.

The objective function is subject to constraints, which are limitations on the values that the decision variables can take. These constraints are also represented as linear equations or inequalities. The constraints and the objective function together form the linear programming problem.

The solution to the linear programming problem is found by applying the simplex algorithm, which involves iteratively improving the solution until the optimal solution is reached. The optimal solution is the set of values for the decision variables that maximises or minimises the objective function while satisfying all the constraints.

In summary, the objective function is a key component of linear programming that represents the goal of the problem. It is a linear equation that is subject to constraints and is used to determine the optimal solution to the problem.