Isoperimetric Problem in Economics
|Author:||Bc. Mikoláš Volek|
|Year:||2011 - winter|
|Leaders:|| doc. RNDr. Oldřich John CSc.
|Work type:|| Bachelors
|Awards and prizes:|
|Abstract:||The isoperimetric problem is one of the broad class of optimal control problems, which draw on the generalization of classical calculus developed in the mid-20th century. In the bachelor's thesis I lay down the mathematical framework that permits to rigorously prove both the necessary and sucient conditions for the existence of a maximizer of the objective function. I analyze a simple problem from the eld of project planning, which is a branch
of applied economics. On the basis of a 1973 article by Cullingford and Prideaux I present an augmented cost function that involves the concept of the time value of money, which is key to proper economic reasoning. I give an explicit solution along with graphical depictions of the impact of a non-zero discount factor on project planing under the model in question. Finally, I introduce additional constraints and discuss the subproblem of multiple equality and non-equality constraints.
|Downloadable:|| Bachelor Thesis of Volek