[1.4] Consider the problem of locating a new machine to an existing layout consisting of four machines. These machines are located at the following coordinates in two-dimensional space: (31),(03),(22), and (14). Let the coordinates of the new machine be (x1x2). Formulate the problem of finding an optimal location as a linear program for each of the following cases: a. The sum of the distances from the new machine to the four machines is minimized. Use the street distance (also known as Manhattan distance or rectilinear distance); for example, the distance from (x1x2) to the first machine located at (31) is x13+x21. b. Because of various amounts of flow between the new machine and the existing machines, reformulate the problem where the sum of the weighted distances is minimized, where the weights corresponding to the four machines are 6,4,7, and 2 , respectively. c. In order to avoid congestion, suppose that the new machine must be located in the square {(x1,x2):1x12,0x21}. Formulate Parts (a) and (b) with this added restriction. d. Suppose that the new machine must be located so that its distance from the first machine does not exceed 2 . Formulate the problem with this added restriction