Consider the following nonlinear programming problem.

max $9$

$2+$

$27+$

s$.$t$.$

$=6$

$>=1,>=1,>=1$

a$)$ Solve by dynamic programming when, in addition to the given constraints, all

three variables are also required to be integers. $(15$ points$)$

b$)$ Use dynamic programming to solve the problem as given $($continuous variables$)$

$(25$ points$)$