d$.(15$ points$)$ Answer the following true$/$false questions. If your answer is "false", provide a brief explanation or a counter$-$example to support your claim.

i$.$ The objective function of a linear programming problem can be a nonlinear function, as long as the constraints are linear.

ii$.$ If an LP problem has more constraints than variables, it is guaranteed to be infeasible.

iii. If the feasible region of an LP problem is unbounded, then the problem will not have a finite optimal solution.