Today, linear programming is typically associated with the works of George Dantzig in 1947. Though some may argue that linear programming was predated long before Dantzig and he alone did not contribute to the subject. Though, this matter can be open for discussion but, one thing for sure, we can agree on is that linear programming hit its peak during WW2. At that time linear programming was used to maximize the efficiency of resources which was something that the military was struggling with.
Purpose & Background of Performing Linear Programming
Linear programming was not just designed to be a qualitative tool to analyse economic phenomena, but more as a method to compute actual answers to specific real-world problems. In simplified economic models, there is linear connection between input variables and output variables. Input variables typically stands for resources and output variables typically stands for commodity. If y is a commodity that is manufactured by the use of resources x1,x2...xn. Then there's a linear correlation given by the equation
y= a1*x1+a2*x2+...+an*xn
where a1,a2...an are constants that say something about the use of the resources in the production. Though the problem with economics is that more than often equations surpasses the amount of variables. Therefore, the equation system couldn’t be solved quite correctly. What Dantzig did, was to rewrite the equations to a system of inequalities.
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