d$.$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.

iiii.Infeasibility means that there are no solutions that can satisfy all constraints simultaneously.

iiiii.If an LP problem has less constraints than variables, it is guaranteed to be infeasible.

iiiiiii.It$$s possible for a linear program to be both infeasible and unbounded.