For the first case do I get y2 correctly and how do I prove if there are multiple optimal solutions

Exercise 5.2. Consider the following LP: 3.2- 6-4 maximise 3x1 - 612 subject to -I1 + 2 2 5x1 + 812 42 X1 - 2x2 3 (5.4) IVIAIA IA 3x1 + 212 21 1, $2 0. (a) Does the problem have multiple optimal solutions? (b) Suppose that we replace the objective function by maximise 6x1+4x2. Are the necessary conditions for the existence of multiple optimal solutions satisfied? Does the problem have multiple optimal solutions in this case? *2 = Xitz 3 X1 - 6*2 8 X2 4 42 - 5X cp parallel to constraint 3 72 ? X1 - 3 2 X 2 = 21 - 3 X ) x1 = ZX2 +3 8 x 2: 42 - 5 ( 2X2+ 3 ) 13 . 1 ) 8X7 : 42 - 10 *7 - 15 2 10 x2 : 27 (3 . 1 4 ) 1 X1 = 42 10 42- 5 . 3 = 27 X12 6 x1 - 8 y. ( - vit X = 2 ) need 4130 8 . 4 : 32 3 vi - 6x2 42 (574+ 8X2 = 42) 3X7 - 6 X2 5 -18 9 - yi + sy = 3 yi + 8 y , = - 6 1341 =-3 42 = - 73 y1 : 20 yi (x, +8 x2 = 42 ) needs yi 20 42 (X1 - 2X 2 = 3 ) 42 20 3x - 6x2 5 9 s Sy + yz = 3 8 41 - 242 : -6 By . : 0 yo = 0 7 implies maybe multiple optimal solutions 2 = 3 took A 0. - 4 unique solution optimal it