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.