Discussion 1 Week 8 Comparing Decision Various and the Objective Function - Assignment Example

Decision Variables and Objective Function al Affiliation Decision Variables and Objective Function What is the relationship between decision variables and the objective function? In solving linear programming problems, two of the most important characteristics or ingredients are the decision variables and the objective function. As defined, the decision variables are “a set of quantities that need to be determined in order to solve the problem; i.e., the problem is solved when the best values of the variables have been identified.

The variables are sometimes called decision variables because the problem is to decide what value each variable should take. Typically, the variables represent the amount of a resource to use or the level of some activity” (What are decision variables?, n.d., p. 1). On the other hand, the objective function represents the aim or goal of the problem being solved: either to maximize or minimize an identified value. The relationship between the decision variables and the objective function, therefore is found in terms of the manner by which each decision variable, identified to be an integral part of the objective function, would contribute towards attainment of the defined goal.

As emphasized, “the objective function indicates how much each variable contributes to the value to be optimized in the problem” (What is the Objective Function?, n.d., p. 1). For example, if the problem calls for maximizing profit (the objective function), then, the decision variables would be to determine how many units ; of product A, product B, or product C to manufacture; given a set of restrictions or constraints, the decision variables would provide the most effective allocation in products to be manufactured in order to maximize profits.2. What is the difference between an objective function and a constraint?

After learning the definition of the objective function, as the main goal or aim to be attained in the linear programming model, a constraint is defined as the “possible values the variables of a linear programming problem may take. They typically represent resource constraints, or the minimum or maximum level of some activity” (What are the Constraints?, n.d.). As disclosed, the constraint takes the following form:Source: What are the Constraints?, n.d. Literally, as the term implies, constraints are restrictions or limitations of resources (time, income, funds, labor, or materials) within which the values in the variables should adhere to.

Thus, the constraints ensure that the objective or goal of the linear programming model is attained given that some restrictions in resources have been integrated in the problem solving process, as required. For instance, in a typical advertising budget problem, the constraints could be the limited amount of funds or budget that could be allocated for various medium: television, print, electronic, or other media which should not exceed, say, 20 advertisements in any of the identified media. Thus, these restrictions should be appropriately satisfied to ensure that the objective function is justifiably attained.

ReferencesWhat are decision variables? (n.d.). Retrieved from courses.psu.edu: https://www.courses.psu.edu/for/for466w_mem14/Ch11/HTML/Sec1/ch11sec1_Vars.htmWhat are the Constraints? (n.d.). Retrieved from courses.psu.edu: https://www.courses.psu.edu/for/for466w_mem14/Ch11/HTML/Sec1/ch11sec1_Constr.htmWhat is the Objective Function? (n.d.). Retrieved from courses.psu.edu: https://www.courses.psu.edu/for/for466w_mem14/Ch11/HTML/Sec1/ch11sec1_ObjFn.htm