2. (21 pts) True/False (please write the entire word "True" or "False"). a.) If a variable in a linear program is defined as nonpositive (e.g. 0), then we can solve the LP using the simplex method by creating and substituting a new variable that is nonnegative (e.g. x = -x 0). b.) If the solution to the Phase I LP has objective function value z = 0, then the original LP is infeasible. For binary variables x and y, "x is not equal to y" can be modeled by the constraint x=y - 1. d.) The feasible region of an integer program is a subset of the feasible region of its LP relaxation. f. e.) If an optimal solution for the LP relaxation is integer-valued, then the LP relax- ation and the IP have the same optimal objective function value. edge. A minimum spanning tree of a network will always include the shortest/least cost g.) For binary variable x and continuous variable y, the statement "If x = 1, then y = 0" can be modeled by the constraint y M(1-x) for arbitrarily large constant M.

2. (21 pts) True/False (please write the entire word "True" or "False"). a.) If a variable in a linear program is defined as nonpositive (e.g. x10 ), then we can solve the LP using the simplex method by creating and substituting a new variable that is nonnegative (e.g. x1=x10 ). b.) If the solution to the Phase I LP has objective function value z=0, then the original LP is infeasible. c.) x=y1. For binary variables x and y, " x is not equal to y " can be modeled by the constraint . The feasible region of an integer program is a subset of the feasible region of its LP relaxation. e.) If an optimal solution for the LP relaxation is integer-valued, then the LP relax-ation and the IP have the same optimal objective function value. f. A minimum spanning tree of a network will always include the shortest/least cost edge. g.) For binary variable x and continuous variable y, the statement "If x=1, then y=0 " can be modeled by the constraint yM(1x) for arbitrarily large constant M