Consider the following optimization problem:

z$*=$ min$($x$^2+$y$)$ exp$($x $-$ y $-3)$

subject to:

x $+$ y $=1$

x $<=3$

y $<=3$

a$)$ what is the set of possible values of x$?$

b$)$ Write the objective as a function of x

c$)$ Write the optimization problem as a univariate optimization

d$)$ Find the optimal solution