1. (10 points) Answer the following five true or false questions in the place provided. Give a brief reason for each answer for a potential part credit of 1 point. (a) The reduced cost for a basic variable is always zero. (b) The dual price associated with a constraint is the improvement in the value of the solution per unit decrease in the right-hand side of the constraint. (c) When the right-hand side value for a constraint changes within the allowable increase/decrease range, the optimal solution stays the same while the optimal objective value changes. (d) An LP is unbounded if, at one iteration during the Simplex method, the coefficients in one row are either negative or zero. (e) Reduced cost can be determined by pricing out