Module 13 : Maxima, Minima and Saddle Points, Constrained maxima and minima
Lecture 39 : Constrained maxima / minima [Section 39.2]
Note that although the set
is not bounded, the set
is closed and bounded, where for some . Further, the minimum of on equals the minimum of on which exists as is continuous. To find this, we solve the equations
Since
we may assume that . Then, it is easy to see that the only common solutions of
for some 
. Further, the minimum of 
on 
equals the minimum of 
on 
which exists as 
is continuous. To find this, we solve the equations 
. Then, it is easy to see that the only common solutions of 
