please solve the following question manually with all steps writen down and detailed. ALL manually please without usung excel or anything else.

Ex. 11 Shown below is a grid layout of a facility complex where there are four existing depart- ments around a central courtyard or circulation space area for material handling and setup and storage. A new facility to service the four departments is going to be located at one of the four points on the grid in the courtyard. You wish to find the location of the new facility {A, B, C, D) that minimizes the total dis- tance traveled in two-way trips to and from the existing departments. The number of two- way trips per day is (10,20,15,30) in that order respectively. Assume that travel is initiated from the central location of the departments, as indicated by their numerical location in the grid. If you wish to minimize the total distance traveled for all departments, which al- ternative location is the best one? 52