Please show all your work, and make sure to justify your answers.

4. Consider the single-facility rectilinear, minisum, location problem. Suppose the location and weight associated with six existing facilities has been given as follows: 1. ( 2 , 2 ) 3 3. ( 9 , 6 ) 3 5. ( 3 , 7 ) 2 2. ( 8 , 7 ) 1 4. ( 1 , 4 ) 1 6. ( 7 , 3 ) 2 (a) Determine the optimum location for the new facility. (b) Suppose the new facility must be 3 or more rectilinear distance units away from each existing facility. Determine the optimum location for the new facility