Also, what is optimal solution and objective value?

Question 4 [10 points). Consider the following integer non-linear programming problem: Maximize Z = 4x} - x + 10x - x Subject to x1 + x2 53 X1,x220 X1, X2 are integers The powers of the decision variables in the objective function are greater than 1, hence it is non- linear. This problem can be reformulated as an integer linear program with six binary variables (11.712, 713. Y21. Yzz, Yzz) defined as follows: if x = ; otherwise' w , where i = 1, 2. a. Reformulate the objective function as a linear function by replacing xi's with yij's. [4 points] (Hint: If xy = 3, i.e, yu3 = 1, then 4x7 - x = 9 = 9y13) b. Reformulate the constraints by replacing xi's with yu's. [4 points