Consider the following linear programming problem.

Max 3 + 3

s.t. + 2 6----------------constraint 1

3 + 2 12-------------constraint 2

, 0

(a)On the graph paper provided in the answer script, draw and label the constraint lines. Hence, mark the feasible region.

(b)Find the optimal solution and optimal value.

(c)Suppose the coefficient of X from the objective function is increased from 3 to 4. Would the optimal solution be changed? Briefly explain your answer by the range of optimality.

(d)Suppose the value of the right-hand side of the constraint 1 is increased by 1 (i.e. from 6 to 7), find the new optimal solution and the dual price for the constraint 1.