Please indicate sub-questions True or False. (Please briefly explain each answer)

a.A linear optimization problem that is neither infeasible nor unbounded must have exactly one optimal solution.

b.At optimality, the shadow price of a non-binding constraint must be zero.

c.A linear optimization problem that is deemed to be infeasible by excel Solver, can be rectified by altering the objective function of the problem.

d.The reduced cost of a decision variable that is not part of the optimal solution, represents the per unit degradation in the objective function if that variable is forced to be part of the solution.

e.The constraint 3*K - 4*J - 5*K*J <= 42, where K and J are variables, is not a linear constraint. However, it is linearizable and can be rewritten as a linear constraint.

f.The branch-and-bound algorithm used to solve integer programming problems, essentially is a technique that solves a series of linear programs with additional constraints and bound checks to arrive at an optimal integer solution.

g.Rounding the decision variables of an LP is a practical way of solving the corresponding integer programming problem. It may not result in the optimal solution but at least it guarantees a good feasible solution.

h.It is impossible for a feasible binary integer program (an integer program with only binary variables) to ever be unbounded.

i.To generate Solver's sensitivity report, excel Solver needs to resolve the problem.

j.Unlike a standard transportation or trans-shipment problem, a Network optimization problem with yield loss or gain is not guaranteed to generate an optimal solution that is integral.