Linear Programming

Linear Programming

     Linear programming is a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.  Or in other words it is the process of taking various linear inequalities relating to some situation, and finding the “best” value obtainable under those conditions.  An example of this would be taking the limitations of materials and labor, and then determining the best production levels for maximal profits under those conditions.  

     From what I have learned the general process for solving linear-programming exercises is to graph the inequalities which are usually called the constraints to form a walled-off area on the x-y plane called the feasibility region.  From there you figure out the coordinates of the corners of this feasibility region.  You find the intersection points of the various pairs of the lines and test these corner points in the formula called the optimization equation; from which you are trying to find the highest or lowest value.  

     From my research I have learned that the history of linear programming goes back as far as the 1940s.  The main motivation for the need of linear programming goes back to the war time when they needed ways to solve many complex problems.  This method which is used to solve linear programming was developed by George B. Dantzig, in 1947.  Dantzig was one who did a lot of work on linear programming.  Dantzig’s discovery of linear programming was through his own personal contribution during WWII when he was working in the Pentagon with the military.  While working one of his friends challenged him by wanting him to speed up certain processes.  While trying to speed up the planning process this is how he discovered linear programming.  

     The importance of linear programming goes to a very high extent and it is now used in many businesses and corporations.  Linear programming is used by business and corporations to allocate resources, plan production, schedule workers, financial problems and also used in military planning which I did not know.  All types of problems can be solved that contain a linear function which can be used to maximize or minimize depending on what the constraints are.  I think using linear programming takes a lot of time to learn and the best place to learn this and what it can be used for are in businesses and corporations.  I had a very hard time this week learning about linear programming and figuring out what I am supposed to do in solving these quantitative methods.  From my own personal research on this method; I think it is pretty cool how this method was made up back in the 1940s.  When I started looking at this method this week I did not know linear programming could be done graphically only in two or three variables, and linear programming using more than three variables requires the use of special algorithms, one of which is the simplex algorithm, which can be found in any text on linear programming.  I also did not know that linear programming in three variables requires that one be able to graph in three dimensions.  Using three dimensions from what I have seen is very popular in today’s businesses.  It is like businesses wants to see their mathematical equations come to life or pop out right at you when trying to solve these problems.  When I get out of the Air Force I am hoping to get a good job with a business or corporation that can teach me this method more in dept.  When it comes to quantitative methods I have a lot to learn and a lot to look forward to when I finally can learn more about businesses and what mathematical methods they use to operate at full capacity when trying to sell their products or services to the open markets.