5 (3) points) Consider\

max_(x,y)g(x,y)=4(x-2)^(2)+3(y-1)^(2)

\ subject to\

x+y=1,AAy.

\ Without solving the problem write down the Kuhn-Tucker conditions.(4) (3points) Consider\

max_(u)\\\\int_0^2 e^(-rt)(2-x(t))dt

\ subject to\

y^()=xy

\

0

and

y(0)=y_(0)>0

\ Without solving the problem, write down the Hamiltonian and the corresponding\ first order condition, especially conditions when

x=1

and when

x=0

.

4. (3points) Consider maxu02ert(2x(t))dt subject to y=xy 0x1 and y(0)=y0>0. Without solving the problem, write down the Hamiltonian and the corresponding first order condition, especially conditions when x=1 and when x=0