Business uses of linear programming
Linear programming is a technique used to make decisions given some conditions or constrain while assuming that the relationship among variables is either linear or non linear. This design helps organization to optimize the allocation of resources. Linear programming is mainly used in formulating product mix that helps to maximize firm profit, minimization of cost during production and in planning. The following methods can be used to find optimal solution in linear programming simplex method, graphical method or the method of computer soft ware’.. Linear programming technique makes several assumptions. First, certainty numbers in objective function do not change during the period and are known without doubt. The third one is the proportionality assumption which permits use of fractions. Lastly only positive variables are considered.
Difficulties in graphical method of solving linear programming models
In graphical methods there are some special cases which occur and pose difficult in solving linear programming problems. This special cases are exhibited when a problem in linear programming region is infeasible, redundant, unbounded or when linear programming problem has multiple solutions. To realize that a linear programming problem has a multiple solutions there are at least two conditions which are clearly seen. Firstly, the objective function should be parallel to the constraint which is forming a boundary on the feasible solution. Secondly, the constraint must be forming a boundary on region of feasibility solutions and in the direction of optimal movement of the linear programming objective function. Regarding linear programming problem having an invisible solution, there is usually no solution (no region) because of conflicting constraints given. Finally, unbounded occur when in the feasible region there are some points with large objective function values. This means that the objective function can be improved without violating any constraint.
The ingredients of linier programming models
There are several essential ingredients of a linier programming model. The first one is decision variables which represents those things which the management can control. The second is constraints, this are mathematical expressions that use variables to express limits. For example a constraint may indicate limited raw materials. Thirdly, there is variable bound which gives the permitted values to be assumed by the linear programming variables. Finally there is the objective function which combines variables to express the linear programming goal.
It is important to understand the characteristics linear programming model. This is because it helps one to develop the objective function as well as the constraint without violating the rules given. It also helps in to visualize how the problem of the organization rhymes with the linear programming problem (Howard, 2009 ).
Differences between maximization and minimization linear programming models
Maximization aims at finding the direction of increase while minimization aims at finding the direction of decrease. In addition, in minimization problem the feasible area may not be bounded to the right but must be bounded in lower left region. In maximization problem the feasible area must be bounded to the top right (Howard, 2009 ). To know whether to apply maximization or minimization model one must consider the under lying facts provided by the organization. Moreover, some statements may even state clearly that the objective of the firm is to either maximize or minimize sales, costs or even profit. Therefore logical thinking and statements provided can give the direction of the model to be used.
References
Howard K. (2009 ). Linear programming. Birkhauser Boston. New York.
