• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

An introduction to linear programming

Extracts from this document...

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.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our AS and A Level Structures, Objectives & External Influences section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Structures, Objectives & External Influences essays

  1. Btec National Business Level 3 Year 1 - Exploring Business Activity

    Regular customer of Microsoft can get a discount price for their interests needs. Oxfam is appreciating to customer because of rising yearly funds event that helps to boost environmental charity scheme. Supplier: Both businesses have to deliver stocks, however the payment of products could be done promptly.

  2. Linear Programming

    The solutions that we calculated by using linear programming would satisfy the given limitations and to enable all resources used in manufacturing-raw materials, labors, facilities are employed most efficiently. The application of linear programming for production scheduling is beneficial because those problems will recur in the next production period; so

  1. Introduction to J Sainsbury plc

    Line organisation is the typical structure of a hierarchy. There are direct communication links between Sainsbury's superiors and subordinates. Each member of Sainsbury's has a clear understanding of the chain of command and to whom he or she is responsible.

  2. Differentiate between strategic planning and operational planning.

    Employment of expertise and professionals: If Mary's Fashion is strong in the market and shows potential for growth then it would be logical that employment of expertise and professionals will be a lot easier compare to a sole proprietorship business that have difficulties rasing capital and employing top professionals.

  1. Business report on J Sainsbury's.

    business are to raise money for the poor and helpless people, also for those with disability and serious illness. Sainsbury's sell product that promote the charity or non-profit campaign and include a donation in their price. Sainsbury's have those objectives because they believe this is one of the main ways that they can maintain their customers.

  2. Business unit 2

    Risk such as lost property/ theft are can be considered high as there are going to be a lot of people attending and their can easy look through people bag and take anything valuable. People can also not have the right attire as the weather is very unpredictable.

  1. Applied Business. Investigating a business Preston Manor High School

    Plus, it costs to print letters out and it cost to send letters through post. This will affect the school budget and the cost of organising a taster day can be expensive. Secondly, it takes time to arrange taster days because the school has to set up classes, prepare class-work and arrange the timings (timetable)

  2. Identify all the considerations that need to be taken into account when planning a ...

    * Monitor evaluator- Monitor Evaluators are fair and logical observers and judges of what is going on. Because they are good at detaching themselves from bias, they are often the ones to see all available options with the greatest clarity.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work