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# An introduction to linear programming

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Introduction

Chapter 1 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."2 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. ...read more.

Middle

inequalities are ?.The region satisfied by all the constraints is the feasible region: any point lying in this region is a possible solution to the problem of optimising the contribution to profit. Figure 1.1 Step 3: Choose arbitrary values. Combine any two of the functions .The writer choose the functions of Line one :8F+5S?1935 (material) and line two:2F+3S?685(hours) to solution it . Assume 8F+5S=1935 and 2F+3S=685. 8F+5S=1935 (1) 2F+3S=685 (2) Let (2)*4 change to :8F+12S=2740. Then use (2)minus(1).Let 7S=805,S=115. And then ,let S=115 put in (2),then 2F+3*115=685 ,F=170. So, the arbitrary values are F=170, S=115. Step 4: Find the profit line and extreme points of the feasible region. Let F=170and S=115 used in the objective function 6F+4.5S. Then, let the objective function equal to 6*170+4.5*115=1537.5�1538. To find the feasible region .Let the objective function 6F+4.5S=1538. When F=0, let 4.5S=1538,then S=341.7�342. Similarly, when S=0,let 6F=1538,then F=256.3�257. F S 0 342 257 0 Next, the writer choose the two function of material and numerals above .so, next according to the point of intersection of this two lines to current position until touch the very edge .To find out the feasible region, the maximize profit. This Assume profit line will show on figure 1.2 Figure 1.2 Step 5: The best solution. It can see that the maximum contribution to profit would occur when produce 170 football jerseys with \$6 and 115 soccer shirts with \$4.5 . ...read more.

Conclusion

Especially in business area it can be used to do the business planning and control. And in conjunction with the case study, it can be seen that this method is also useful in developing manufacture plans as producing the jerseys and shirts for the youth teams. In conclusion, these scientific approaches to solving problems are easy way to find out the best profits for a manufacture. Linear programming is the most useful method in making decision no matter the variable will be changed or not. This model can consider those problems that require the most creative attention. Linear programming is a useful model suggesting that management must continually evaluation its original investment decision. No matter how the variables are changed under certain conditions, the linear programme is aiming at finding out the best way to achieve profits as far as possible in order to run the organization with optimum profits. REFERENCE 1. http://www.markschulze.net/LinearProgramming 2. Terry I. Dennis and Laurie B.Dennis (1991) management Science New York: West publishing company BIBILOGRAPHY 1. R. D. Seale&A. D. Sealejr& Jason Leng(2004) An application of business activity modeling to regional production and national distribution of plywood. Forest Products Journal VOL. 54, No. 12 2. Anderson,D.R.,D.J.Sweeney ,and T.A. Williams.(1974) Linear programming for decision making .St.Paual:West publishing 3. Burke,R.,(1995)Project Management-planning &control ,wiley ,London 1 http://www.markschulze.net/LinearProgramming 2 Terry l.Dennis and Laurie B.Dennis (1991) management Science New York: West publishing company 2 Terry l.Dennis and Laurie B.Dennis (1991) management Science New York: West publishing company ?? ?? ?? ?? 1 ...read more.

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