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1. [20 Pt.) An optimization programming model is formulated as follows: s. t. Max. Z = x + 2y 3x + y 2 3 x + 3y = 2 - x + 2y 2 5x + y = 15 2x -y s4 x,y20 and the constraints in the model are illustrated in a plot as B E D F H K M N (1) [5 Pt.] As an LP problem, identify the feasible solution area. (11) [5 Pt.) Which points are the extreme points? Find the coordinates of each extreme point. (iii) [5 Pt.] In the feasible solution area in (1), 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 and Zip in IP, respectively