Given the feasible optimal solution of an LP below: Z x1 x2 x3 s1 s2 s3 RHS 0 8 10 0 4 0 1 0 1 -4 -2 0 0 2 6 0 1 0 0 -5 -1 0 10 7 0 0 0 10 0 6 1 a) What are the basic and nonbasic variables? (5 pts) b) What are the primal and dual optimal solutions? (10 pts) c) Write the mathematical model of your primal LP for the values that you can be sure of. What other information do you need to fill the missing parameters of the original LP? (15 pts) d) Which constraints of the primal model are binding? Why? (15 pts) e) Now, assume that the dual of this LP is unbounded. What could be inferred from this and the optimal solution above? (15 pts) f) Considering part (e) and having non-negativity constraints for all of the primal variables, is it possible to apply the Dual Simplex Method? If so, what are the entering/leaving varibles and the pivoting element? If not, why? (15 pts) Hint: Si refers to the slack variable of the ith