Optimal Time to Attain a Targeted Profit Function Under Unitary Transformation

Abstract

The problem of fastest descent is solved by the calculus of variations which is a branch of mathematics dealing with the optimization problem of physical quantities. In this paper, profit maximization problems are judged by using this idea. In an economic system profit velocity and time are key factors to optimize policy. That is why we have investigated the path of the profit function and the minimum time to reach the final destination of a profit function by utilizing a unitary operator. Given two states, the starting profit function and the targeted profit function, there is a path which optimizes the economic policy in a least possible time among different paths. This investigation uses the unitary transformation, which transforms the starting profit function to the targeted profit function in the least possible time.