How do you maximize and minimize #f(x,y)=xy-y^2# constrained to #0<x+3y<4#?

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Answer 1 · 2017-01-16T17:32:47

#((x,y,f(x,y),"type"),(0,0,0,"maximum"),(1,2.5,0.5,"maximum"))#

Using the Lagrange Multipliers technique the relative minima/maxima to this problem can be determined.

Those are

#((x,y,f(x,y),"type"),(0,0,0,"maximum"),(1,2.5,0.5,"maximum"))#

Attached a plot showing those points located at the feasible region frontier.

enter image source here