1. [25 Pt.] An optimization programming model is formulated as follows: Max. Z= x + 2y s.t. 3x + y 23 x + 3y = 2 - x + 2y 0 and the constraints in the model are illustrated in a plot as A , C E D F G H 1 K L M N -2 (1) [5 Pt.) As an LP problem, identify the feasible solution area and shade it above graph. (ii) [5 Pt.] Which points are the extreme points? Find the coordinates of each extreme point. (iii) [5 Pt.] In the feasible solution area in (i), identify all the possible integer solution points as an IP problem. (iv) [5 Pt.] Based on (iii), compute the optimal objective values Zip in LP. (v) [5 Pt.] Based on (iii), compute the optimal objective values Zip in IP