Consider the problem of locating a new machine to an existing layout considering the position of four machines. These machines are located at the following coordinates of a plane: (3,0), (0,-3), (2,1), and (1,4). Let the coordinates of the new machine be (x1,x2). Formulate the problem of finding an optimal location for the new machine as a linear program given that the objective is to minimize the sum of the distances from the new machine to the four existing machines. Use the “street” distance (rectilinear norm); for example, the distance from (x1,x2) to the first machine located at (3,0) is absolute (x1-3) + absolute (x2-0). In your formation, clearly define the variables, and state the objective function and constraints with proper justification.

# Consider the problem of locating a new machine to an existing layout considering the position of four machines. These machines are located at the following coordinates of a plane: (3,0), (0,-3), (2,1), and (1,4). Let the coordinates of the new machine be (x1,x2). Formulate the problem of finding an optimal location for the new machine as a linear program given that the objective is to minimize the sum of the distances from the new machine to the four existing machines. Use the “street” distance (rectilinear norm); for example, the distance from (x1,x2) to the first machine located at (3,0) is absolute (x1-3) + absolute (x2-0). In your formation, clearly define the variables, and state the objective function and constraints with proper justification.

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