1. [25 Pt.] An optimization programming model is formulated as follows: Max. Zx+2y s. t. 3x + y 3 x + 3y 2 - x + 2y 2 5x + y 15 2x - y 4 x, y 0 and the constraints in the model are illustrated in a plot as A E F C B D G H K L N M (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.