Consider the following LP, Given the following maximization problem, Pl: Max 3x + 4x2 + x3 + 5x4 s.t. X + 2x2 + x3 + 2x4 35 2x2 + 3x2 + x3 + 3x4 58 X, 30,X, 2 0,X3 2 0,X4 50 a) [10 points] Find its corresponding dual program [D]. b) [10 points] Find the optimal solution of the dual by any method (e.g., Simplex, Graphical, etc.). (Hint: chose the method carefully, which can save a lot time and efforts.) c) [Bonus 10 points] Find the optimal solution to primal problem [P]. (Hint: chose the method carefully, which can save a lot time and efforts.)