In linear programming problems the function whose maxima or minima are...
In linear programming problems the function whose maxima or minima are to be found is called Objective function .
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In linear programming problems the function whose maxima or minima are...
Objective function:
The objective function in linear programming problems is a mathematical representation of the quantity that needs to be maximized or minimized. It is denoted by \( f(x_1, x_2, ..., x_n) \), where \( x_1, x_2, ..., x_n \) are the decision variables. The goal is to optimize this function while satisfying certain constraints.
Role in linear programming:
- The objective function plays a crucial role in linear programming as it defines the goal of the optimization problem.
- It serves as a measure of performance or effectiveness that needs to be optimized.
- The objective function can be in the form of maximizing profits, minimizing costs, maximizing efficiency, etc.
Maximization or minimization:
- In linear programming, the objective function can either be maximized or minimized based on the requirements of the problem.
- The decision variables are adjusted to achieve the optimal value of the objective function.
Constraints:
- The objective function is subject to certain constraints represented by linear equations or inequalities.
- These constraints limit the feasible solutions that can be obtained for the objective function.
Optimal solution:
- The objective function helps in finding the optimal solution that maximizes or minimizes the function within the given constraints.
- The solution obtained through linear programming provides the best possible outcome for the objective function.