The Von Trapp family is in the process of moving to a new city where both parents have accepted new jobs. In trying to find an ideal location for their new home, the Von Trapp's list the following goals:
(a) It should be as close as possible to Mrs. Von Trapp's place of work (within 1/4 mile).
(b) It should be as far as possible from the noise of the airport (at least 10 miles).
(c) It should be reasonably close to a shopping mall (within 1 mile).
Mr. and Mrs. Von Trapp use a landmark in the city as a reference point and locate the (x, y)-coordinates of work, airport, and shopping mall at (1, 1), (20, 15), and (4, 7), respectively (all distances are in miles). Formulate the problem as a goal programming model.