Problem 1: Suppose you have eight binary decision variables X1, X2, ..., xg in an integer-linear program (ILP). Please explain how you would incorporate the following restrictions into an ILP. It is acceptable to add variables and/or constraints. Part a: If X5 = 0, then x2 = 1. Part b: If x4 = 0, then x1 = 1 or X5 = 1. Part c: It is unacceptable to have both X2 = 1 and X4 = 0. Part d: At least three out of eight decision variables must take the value of zero. Parte: If either Xg = 1 or x6 = 0, then x2 = 1. Part f: If X3 = 1 and xs = 1, then neither x2 nor X7 can take the value of 1. Part g: If x1 = x2 = x3 = X4 = 1, then x6 = 1. Part h: Li=1 Xi is equal to 0, 2, or 7. Part i: At least two of the following inequalities are satisfied: X1 + X5