bounds relaxations and graphical solution method

(34 points) Bounds, Relaxations, Graphical solution method: Consider the following problem: max 233+y s.t. 433+y S8 223+y Z3 113+4y S8 33,;9 EZ (a) (2 points) Is the problem convex? Justify your answer. (b) (2 points) Is the solution (as, y) : (1,4) feasible? (c) (2 points) Is the solution (2;, y) : (1,1) feasible? ((1) (2 points) Is the solutiotn (:17, y) : (1.5,0.5) feasible? ) (e (2 points) What is the value of the objective function that corresponds to each of the previous three solutions? (f) (4 points) Does each of these three values correspond to a lower bound, upper bounds, none, or both (Note, the problem is a maximization problemI)? (g) (2 points) Eliminate the last constraint (integrality of a: and y) to create a relaxation of the original problem. Is the new relaxation problem convex? (h) (2 points) Are the solutions above feasible for the relaxation? (i) (4 points) Are the three objective function values lower bounds, upper bounds, none, or both, for the relamation? (j) (10 points) Solve the relaxation by the graphical method. (k) (2 points) What does the optimal value of the relaxation give you in terms of the original (non covex) problem (with integrality constraints)