Non-linear dynamical system of differential equations describing the process of production and sales of some consumer good.

摘要

This paper is to demonstrate the use of higher-level mathematics to solve an economics problem in maximizing profit of a daily demand commodity when there is no competition.;A system of differential equations from Gorskii's work is discussed, and the shortcomings of his solution (i.e. boundedness of some of the parameters), stating that this is a problem in optimal control, rather than calculus of variation. Theoretical proofs of Dr. Ellina Grigorieva are discussed and interpreted.;Numerical analysis methods with reasonable values used for the parameters are used to look at graphs of the system.;Mathematically, the form of the solution is found. Economically, possible production plans can be predicted and those that cannot maximize profit rejected.