Explain how to solve the following problem in linear (expected) time. This problem can be modeled as a linear programming (LP) problem, perhaps with some additional pre- and/or post- processing. Explain how the problem is converted into an LP instance and how the answer to the LP instance is used/interpreted to solve the stated problem. You are given two point sets P = {p_1, ..., p_n} and Q = {q_1, ..., q_m} in the plane, and you are told that they are separated by a vertical line x = x_0, with P to the left and Q to the right (see figure on next page). Compute the line equations of the two crossing tangents, that is, the lines l_1 and l_2 that are both supporting lines for CH(P) and CH(Q) such that P lies 3 below l_1 and above l_2 and the reverse holds for Q. (Note that you are not given the hulls, just the point sets.) Your algorithm should run in O(n + m) (expected) time