▁built ▁his ▁model ▁of ▁input - output ▁analysis ▁from ▁the ▁' material ▁balance ' ▁tables ▁constructed ▁by ▁Soviet ▁econom ists , ▁which ▁themselves ▁followed ▁earlier ▁work ▁by ▁the ▁phys i ocr ats . ▁ ▁With ▁his ▁model , ▁which ▁described ▁a ▁system ▁of ▁production ▁and ▁demand ▁processes , ▁Le ont ief ▁described ▁how ▁changes ▁in ▁demand ▁in ▁one ▁economic ▁sector ▁would ▁influence ▁production ▁in ▁another . ▁In ▁practice , ▁Le ont ief ▁ ▁estimated ▁the ▁coefficients ▁of ▁his ▁simple ▁models , ▁to ▁address ▁econom ically ▁interesting ▁questions . ▁ ▁In ▁production ▁econom ics , ▁" Le ont ief ▁techn ologies " ▁produce ▁outputs ▁using ▁constant ▁proport ions ▁of ▁inputs , ▁regardless ▁of ▁the ▁price ▁of ▁inputs , ▁reducing ▁the ▁value ▁of ▁Le ont ief ▁models ▁for ▁understanding ▁econom ies ▁but ▁allowing ▁their ▁parameters ▁to ▁be ▁estimated ▁relatively ▁easily . ▁In ▁contrast , ▁the ▁von ▁Ne umann ▁model ▁of ▁an ▁expand ing ▁economy ▁allows ▁for ▁choice ▁of ▁techniques , ▁but ▁the ▁coefficients ▁must ▁be ▁estimated ▁for ▁each ▁technology . ▁ ▁Mathemat ical ▁optimization ▁ ▁In ▁mathematics , ▁mathematical ▁optimization ▁( or ▁optimization ▁or ▁mathematical ▁programming ) ▁refers ▁to ▁the ▁selection ▁of ▁a ▁best ▁element ▁from ▁some ▁set ▁of ▁available ▁alternatives . ▁In ▁the ▁simplest ▁case , ▁an ▁optimization ▁problem ▁ ▁involves ▁maxim izing ▁or ▁minim izing ▁a ▁real ▁function ▁by ▁selecting ▁input ▁values ▁of ▁the ▁function ▁and ▁computing ▁the ▁corresponding ▁values ▁of ▁the ▁function . ▁The ▁solution ▁process ▁includes ▁satisfying ▁general ▁necessary ▁and ▁sufficient ▁conditions ▁for ▁optim ality . ▁For ▁optimization ▁problems , ▁special