Cake eating problem
Example
Solve the cake eating problem for theu(x)$lnxfunction.
Observe that in this formulation one can use the logarithmic function as it
is perfectly legitimate in the Kuhn-Tucker theory as in this case one has a
convex open setU over which the whole story of optimization is
considered. The Euler equation is
1
ct
=β^1
ct+ 1
,t= 1 , 2 ,.. .,T 1.
and we also haveλ>0 andwT+ 1 =0 that is
T
∑
t= 1
ct=w 1.