Objective function is prominently used to represent and solve the optimization problems of linear programming. The objective function is of the form Z = ax + by, where x, y are the decision variables. The function Z = ax + by is to be maximized or minimized to find the optimal solution. Here the objective function is governed by the constraints x > 0, y > 0. The optimization problems which needs to maximize the profit, minimize the cost, or minimize the use of resources, makes use of an objective function. Show
The objective function is used across industry, commerce, management, applied sciences to solve numerous real-life problems. Let us learn more about solving the objective function, its theorems, applications, with the help of examples, FAQs. What Is Objective Function?The objective function is needed to solve the optimization problems. A linear representation of the form Z = ax + by, where a, b are constraints, and x, y are variables, which have to be maximized or minimized is called an objective function. The variables x and y are called the decision variables. An objective function is governed by a few constraints, some of which are x > 0, y > 0. Objective Function: Z = ax + byObjective function of a linear programming problem is needed to find the optimal solution: maximize the profit, minimize the cost, or to minimize the use of resources, right deployment of resources. Objective function in LPP has wide application in representing problems of commerce, industry, and applied sciences. Terms Related To Objective FunctionThe following terms help in easily understanding the concept of the objective function
Theorems Of Objective FunctionThe two important theorems of the objective function of a linear programming problem are as follows.
Solving An Objective FunctionThe feasible region of the objective function of a linear programming problem is obtained by forming a graph of the objective function, finding the corner points, and then finding the maximum and minimum values. Let us try to understand this in the below steps.
Application Of Objective FunctionThe objective function has great application in functions that are used for optimizing the profits, minimizing the cost, and making optimal use of limited resources. The various applications of the objective function are as follows.
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Examples of Objective Function
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FAQs on Objective FunctionAn objective function is a linear equation of the form Z = ax + by, and is used to represent and solve optimization problems in linear programming. Here x and y are called the decision variables, and this objective function is governed by the constraints such as x > 0, y > 0. The objective function is used to solve problems that need to maximize profit, minimize cost, and minimize the use of available resources. How To Solve An Objective Function?The objective function Z = ax + by is generally solved graphically. The graph of an objective function is a line and the constraints and the axis lines in the coordinate plane together form the feasible region. The corner points are identified and the same is substituted in the objective function to find the maximum value M and the minimum value m, of the objective function. Why Do We Call It An Objective Function?The objective function is referred to by this name since it is used to find the optimal solution of a linear programming problem. The objective function is solved to find the maximum or minimum value, by graphing functions in the coordinate system. Where Do We Use The Objective Function?The objective function is used in problems where the decision variables have constraints. The problem of minimizing the cost, maximizing the profits, within the limited resources is easily solved by representing them as linear equations. The objective function is widely used in commerce and industry, management, applied sciences. Write A Few Examples Of Objective Function?The objective function is prominently used in manufacturing problems, diet problems, logistic problems. The limitation of machine time, limited man hours, warehouse space, are the constraints that are applied to an objective function to solve the manufacturing problem. The right proportion of diet with the required number of nutrients and at a low cost is to be solved as an objective function. For solving the logistics problem, we need to consider the right route, to reduce the fuel cost and time, and find the optimal solution of the objective function. |