Consider the linear programming problem minimize c1x + c2y subject to x + y ? 4 x + 3y ? 6 x ? 0, y ? 0 where c1 and c2 are some real numbers not both equal to zero.

(a) Give an example of the coefficient values c1 and c2 for which the problem has a unique optimal solution.

(b) Give an example of the coefficient values c1 and c2 for which the problem has infinitely many optimal solutions.

(c) Give an example of the coefficient values c1 and c2 for which the problem does not have an optimal solution.