Locating pleasant facilities, such as parks, hospitals, and fire stations, is often done in a man- ner that minimizes the expected traveling distance for patrons. Likewise, locating unpleasant facilities, such as sewage treatment plants or high power cables is often done in a manner to maximize the expected distance. (a) Consider locating a pleasant facility on a road of length a where demand position X that occur are located as U (0, a) random variables. What is the position of the facility on the raod x0, such that E (X – xol) is minimized? (b) Where should the facility be located for any arbitrary demand distribution with proba- bility density function f(x) defined on the length of the road? (c) Where should the facility be located for any artitrary demand distribution with proba- bility mass function f(x) defined on the length of the road?