# Objective Function vs Constraints in Linear Programming

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Linear Programming Model in Operation Research study is usually mathematical type of model which contains set of equations that represent objective function and constraints. The keywords in this article are Objective Function and Constraints, according to Heizer & Render (2008) Objective Function are mathematical expression expressed in linear programming designed to maximizes or minimizes some quantity, for example profit can maximized while the cost might be reduced. The objective function is also called effectiveness function, it is the mathematical expression of the objectives which may be cost of operation or profit on operation (Kumar and Hira, 2008). Constraints which is also known as restrictions are mathematical expressions of the limitations that are involved in fulfilling the objectives; they are caused by scarce or limited resources which may include money, space, manpower, materials and so on. Heizer & Render (2008) defined constraints as restrictions which limit the extent to which a manager can pursue an objective The objective function is more important than the constraints in a linear programming model under the circumstances in which the controllable variables which is also called the decision variables forms the major components of the linear programming model. Controllable variables are the variables that are directly under the control of the operations analyst; their values are determined by the solution of the problem. Using the stock control or inventory as an example, the controllable variables are the order size and the interval between the placed orders (Kumar and Hira, 2008). On the other hand the constraints are more important than the objective function in linear program model when the models function depends largely on the uncontrollable variables of the model. They are variables that are the function of the external environment and over which the operations analyst has no control, such variables are known as state of nature. Using the transportation system as an example, the per unit transportation cost is known as uncontrollable variable because it is subjected to continuous, unceasing change. In conclusion, it is imperative to understand and analyses the situation carefully before applying one linear programming over the other in other to improve or optimize current operations (Heizer & Render, 2008). Furthermore, it is difficult to predict or choose without examining several samples, the more reason why it is important to define variables which represent the problem from the real world, then based on the variable determine the most applicable method (Heizer & Render, 2008).

References:

Heizer, J. & Render, B. (2008) Operations Management and Principles of Operations Management. PowerPoint presentation, 7th Edition. Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Kumar, G.P. and Hira D.S. (2008). Operations Research, Revised Edition. Chand and Company Ltd., New Delhi.