What is a decision variable in a linear programming model?

In a linear programming model, a decision variable represents the elements that decision-makers can control to achieve the best outcome according to a certain objective function. Specifically, these variables are used to denote the quantities of resources, products, or activities that need to be determined in order to optimize an objective, such as maximizing profit or minimizing costs.

By definition, decision variables are controllable input variables. They can be adjusted or manipulated within the constraints of the model to find the optimal solution. For example, in a manufacturing problem, decision variables might represent the number of units to produce for different products, which can be changed based on the constraints of resource availability and market demand.

Understanding the role of decision variables is crucial in linear programming, as they form the basis for formulating the optimization problem and directly influence the results produced by the model. This distinct characteristic differentiates them from other components of the linear programming framework, such as constraints and objective functions, which play supporting roles in defining the relationships and goals of the model.