University of the Atlantic is moving its business school into a new building, which has been designed to house six academic departments. The average time required for a student to get to and from classes in the building depends upon the location of the department in which he or she is taking the class. Based on the distribution of class loads, the dean has estimated the following mean student trip times in minutes given the departmental locations. (i) Find the optimal assignment of departments to locations to minimize mean student trip time in and out of the building. (ii) What is the optimal mean student trip time? ( 10 points)