1. [30 Pt.] A linear programming problem is given as follows: Minimize = 41 + 2 Subject to 81 + 22 16 41 + 22 12 1 5 2 2 1, 2 0 (i) [5 Pt.] Find the A, B, C, D and E, F, G, H, K points on the plot below. (ii) [5 Pt.] Identify the feasible solution area graphically on the following plot (by shading the area). (iii) [5 Pt.] Which points are the extreme points? (iv) [5 Pt.] What is the solution of the optimization problem? (x1=?,x2=?,z=?) (v) [5 Pt.] Which change will make the problem have multiple optimal solutions? a) Increase of the coefficient of 1 on the objective function to 4 b) Increase of the coefficient of 1 on the objective function to 2 c) Decrease of the coefficient of 1 on the objective function to -8 d) Increase of the coefficient of 2 on the objective function to -8 e) None (vi) [5 Pt.] If a new constraint, 2 14, is added to the given problem, what effect will be? (Choose all the effects) a) The feasible solution area will be smaller. b) The feasible solution area will be larger. c) The given problem becomes infeasible. d) The optimal point will be changed. e) The objective value will be decreased. f) There will be no effect.

x2 F E D A B (0,0) x1 G H