(P) 7. Consider the following linear programming problems (P) and (D): max 3.31 + 2 + 2.r3 min 5dy + y2 + y3 s.t. 2x1 + ar2 3 2 + 3x3 = 1 ay + y21 exi +43 21 3y2 + y2 = 2 (D) 21,220, VI 20,93 So, 23 unrestricted, Y2 unrestricted, where a, d and e are real numbers with a > 0. Suppose that the problem (D) is the dual of the problem (P), with Y, y2 and y3 being the dual variables corresponding to the first, second and third linear constraints of (P), respectively, and that the dual problem (D) has an optimal solution y = (a, a,b), where b is a real number. (a) What are the values of d and e? Explain. (10 marks) (b) Find the optimal value and solution of the primal problem (P). (10 marke (P) 7. Consider the following linear programming problems (P) and (D): max 3.31 + 2 + 2.r3 min 5dy + y2 + y3 s.t. 2x1 + ar2 3 2 + 3x3 = 1 ay + y21 exi +43 21 3y2 + y2 = 2 (D) 21,220, VI 20,93 So, 23 unrestricted, Y2 unrestricted, where a, d and e are real numbers with a > 0. Suppose that the problem (D) is the dual of the problem (P), with Y, y2 and y3 being the dual variables corresponding to the first, second and third linear constraints of (P), respectively, and that the dual problem (D) has an optimal solution y = (a, a,b), where b is a real number. (a) What are the values of d and e? Explain. (10 marks) (b) Find the optimal value and solution of the primal problem (P). (10 marke