Consider the problem of locating a new machine to an existing layout consisting of two machines. These machines are located at the following X1 and X2 coordinates:(3,0) and (1.-2).
Let the coordinates of the new machine be (X1,X2).
(a) Formulating the problem of finding an optimal location as a linear programming problem so that the sum of the distance from the new machine to the two machines is minimized. Note: use the Manhattan distance; for example, the distance from (X1,X2). to the first machine located at (3,0) is |X1-3| + |X2|.
(b) Because of various amounts of flow between the new machine and the existing machines, we want reformulate the problem where the weighted distances is minimized. Explain how to modify the previous formulation using the weights for the two machines are 3 and 1.
(c) Suppose that the new machine must be located so that its distance from the first machine does not exceed 3/2. Write constraints to apply this restriction.