Graphical Illustration of Bivariate Constrained Optimization

choose function

x+y

xy

2

x

-

2

y

move point

cylinder

axes

boxed

surface opacity

This Demonstration illustrates graphically finding a constrained extrema of a function of two variables

z=f(x,y)

with a constraint

g(x,y)=0

. In this Demonstration

g(x,y)=

2

x

+

2

y

-1

. While the brown point moves on the unit circle, the cyan point moves on the curve, which is the intersection of the surface that is the graph of the function

f

and the cylinder given by

z=g(x,y)

.