The following simplex tableau shows the optimal solution of a linear programming problem. It is known that x4 and X5 are the slack variables in the first and second constraints of the original problem. The constraints are of the = type (the z-row is the negative reduced costs) X1 X4 RHS 1 0 -2 4 -35 X3 0 0 1/4 1 1/4 3/2 -1/2 0 -1/6 1/3 2 Z xg Z 0 -2 0 X1 0 1 a. Write the original problem. b. What is the dual of the original problem? c. Obtain the optimal solution of the dual problem from the tableau.