Homework Four Please submit the .ipynb file(s) on eCampus. Problem 1 (30 pt.) Solve the following linear programs using Python and Gurobi: (1) max z = 4x1 + 2x2 s.t. x1 ≤16, x1 + 3x2 ≤15, X2 ≤ 5, X1, X2 ≥0 (2) max s.t. z = 2x1 + 4x2 + 3x3 x1 + 3x2 + 2x3 ≤ 30 x1 + x2 + x3 ≤ 24 3x1 +5x2 + 3x3 ≤ 60 (3) min z = −3x1 + x2 + x3 s.t. x1 - 2x2 + X3 ≤ 11, - 4x1 + x2 + 2x3 ≥ 3, - 2x1 + x3 = 1, X1, X2, X30 (4) min z = 15x1 + 20x2 s.t. x1 + 2x2 ≥ 10, 2x1 -3x2 ≤6, x1 + x2 ≥ 6, X1, X2 ≥0 1