please help!

can please you just answer the first 5 T/F

True or False? 1. A CPF solution is the only optimal solution if none of its adjacent CPF solutions are better. 2. If a feasible solution is optimal but not a CPF solution, then infinitely many optimal solutions exist. 3. If an LP problem has 2 decision variables and 2 constraints (not including non-negativity constraints), then the number of CPF solutions could be as many as 6 . 4. Between the primal and dual problems, both W (objective function value in dual) and Z (objective function value in primal) will reach the same value in the optimal solution. 5. If a slack variable is needed to convert a primal constraint to a standard constraint in a maximization problem, the corresponding dual variable will be restricted to negative. Find the best or the closest answer (You are allowed to use a computer in this part) Consider the following problem. Let x4,x5,x6 denote the slack variables for the respective constraints. After applying the simplex method, a portion of the final simplex tableau is as follows: 6. What is the value in blank a ? (a) 0 (b) 1 (c) 2 (d) 3 (c) 4 (f) 5 (g) 6 (h) 7 7. What is the value in blank b ? (a) 0 (b) 1 (c) 2 (d) 3 (c) 4 (f) 5 (g) 6 (h) 7 8. What is the value in blank c ? (a) 0 (b) 1 (c) 2 (d) 3 (c) 4 (f) 5 (g) 6 (h) 7 9. What is W ? (a) y1+3y2y3 (b) 6y1+y2+2y3 (c) 2y1+3y2+y3 (d) 2y12y2+2y3 10. What is the sign restriction about yi (for i=1,2,3 ) in the dual? (a) non-ncgative (b) non-positive (c) unconstrained (d) cannot be determined