An introduction to linear programming
This assignment is mainly about linear programming model of business planning and control. Linear programming which is a relatively young mathematical discipline. It is dating from the invention of the simplex method by G. B. Dantzig in 1947. 1 Linear programming is used in economics and management. Linear programming is the most useful and frequently used problem solving tools. It has been defined as that “linear programming is mathematical solution technique that enables manger to make decisions concerning the best use of an organization’s resources.
@This model is always used in many industries to maximize or minimize some quantities (for example: profit, costs.) Mathematically, the linear programming models usually maximize or minimize an objective function subject to a set of constraints. The goal of this literature is to find the best possible solution. At last, it can be found the best possible solutions so that the objective function is maximized or minimized within the given constraints.
The basic format of linear programming is to find an objective function of a maximum or minimum functions first. This function is the finally resulted. And then according to the conditions of the case to identifying the other functions, every optimal solution to both problems can be characterized by setting their objectives equal to one another gather their respective constrains. E. g. : Max: aX+bY 1. Subject to: 1. cX+dY? I 2. eX+fY? J 3. gX+hY? K
The strengths of linear programming are that it can easily find the solutions for complex problems. Using liner programming can search the most feasible solutions. The linear programming can let manger to make the decision easily. The decision-maker is required to approach the problem in an orderly sequence and remove all unrelated factors from consideration. Using the linear programming the ultimate goal in the problem is the maximization of profit.
Using this method in real business, the plans of sales in each department are clearly defined, and it can help to pinpoint those key factors contributing mostly to the department’s plan with greater profit. The Weaknesses of linear programming is that it is Problems solving techniques, this means that it may determine a certain property of the model. The linear programming needs to consider an aim of maximizing the objective function. In addition to the objective function, some of them were very simple.
The interactions between variables such as that there are alternative courses of action or a variety of solutions available For business area, this model commonly used to analysis pure competition, which assumes may buyers and sellers in the market. Linear programming can let the manger make decision to choose the opportunities facing an organization regarding the optimum use of its long-term resources to change from one time period to another. To make the best decision, it is important choose the best profit to run the organization.