For This Problem, Indicate True Or false and give a brief reasoning Thank You

(a) [1pt] Consider a standard LP with four variables and three constraints. Suppose (0,0,0,4,0, 12, 18) and (3,0,0,1,0,2,0) are two basic feasible solutions of the augmented form of the LP. Then their corresponding CPF solutions (of the standard LP) must be adjacent. (6) [1pt] If a linear program has no optimal solution, then it must have an unbounded feasible region. (c) [1pt] Consider the shadow prices of a standard form of LP. The vector formed by the shadow prices is an optimal solution of the dual problem of this LP. (d) [1pt] A linear program can have exactly 10 feasible solutions. (e) [1pt] Consider a primal problem of maximizing c? x and a dual problem of minimizing by (both subject to some constraints). If for a primal feasible solution x and a dual solution y, we have c? x > by, then y must be dual infeasible (i.e. not a feasible solution of the dual problem). (f) [1pt] If a linear program is feasible, then its dual problem must be feasible