Consider the following nonlinear programming problem.

max$9x-x^2+y^2-7y+z$

s$.$t$.$

$xyz=6$

$x1,y1,z1$

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$).$