Label each of the following statements about linear programming problems as true or false, and then justify your answer.

(i). Use optimality test. In minimization problems, "better" means smaller. To see this, note that min Z = – max (–Z).

(ii). CPF solutions are not the only possible optimal solutions, there can be infinitely many optimal solutions. This is indeed the case when there are more than one optimal solution. For example, consider the problem

maximize         Z =      x₁+ x₂

subject to                     x₁ + x₂≤ 10

x₁, x₂≥ 0

where Z* = 10, x^*₁= k and x^*₂= 10 – k with k € [0, 10] are all optimal solution.

(iii). However, this is not always true. It is possible to have an unbounded feasible region where an entire ray with only one CPF solution is optimal.