Exploring optimization through hierarchies and ratio scales

This paper explores the concept of optimization by solely using the AHP and compares outcomes with those obtained in traditional optimization theory without and with constraints. The difference is essentially in the absence of the traditional black box involving complex manipulations in algebra or the calculus on an assumed linear or nonlinear mathematical structure. This paper is an exploratory attempt to use an individual's understanding together with a way to convert his judgments to ratios to deal with optimization. At first sight it may go contrary to the reader's (learned) intuition, but in the end he must face the question of whether the magic of traditional manipulations gives rise to better answers than one's actual and complete understanding in which one does not abdicate judgmental control of the solution, and why. This idea is ripe for deeper and more detailed exploration.