DISCUSSION 2 3

Discussion2

Ina linear programming model, there are decision variables, objectivefunction, and constraints. An objective function entails amathematical expression of the decision variables that are present ina linear programming model (Vaserstein & Byrne, 2003). It is notpossible to have an objective function before first of all having thedecision variables. Decision variables are a representation of thechoices available to a decision maker these are presented in termsof amounts of their outputs or inputs (Vaserstein & Byrne, 2003).Every unknown quantity is usually assigned a decision variable. Forexample, decision variables may be represented as x_{1},x_{2},x_{3,}depending with the number of variables required in the model. Thereare two types of objective functions minimization or maximizationobjective function.

Onthe other hand, constraints describe limitations, which tend torestrict the alternatives available a decision maker. There are threetypes of constraints equal to constraint, less than or equal toconstraint, and greater than or equal to constraint. A less than orequal to constraint implies an upper limit on the amount of aresource is available for use while a greater than or equal toconstraint implies that there is a certain minimum that has to beattained. Alternatively, an equal to constraint implies that aspecific or exact amount of a resource is required (Vaserstein &Byrne, 2003). A constraint may not refer to all variables present ina model because constraints depend with the available resources.Depending with the resources available, constraints may change.

Considerthe constraint 8x + 2y ≤ 20

Inplotting this constraint, one can consider graphing the equation ofthe line 8x + 2y = 20.After graphing this equation, one can pick a point below and abovethe line in order to establish the point that satisfies the desiredregion. After getting the wanted region, the unwanted region isshaded.

References

Vaserstein,L. N., & Byrne, C. C. (2003). *Introductionto linear programming*.Upper Saddle River N. J.: Pearson Education.