A sensor problem

A security company has placed 4 sensors in a one story house. Using the southwest corner of the house as the origin, the locations of the sensors are (2,1), (10,5), (11,25), and (5,30). The problem the company now has is to place a central unit to collect the sensor data and collects data. The company would like to minimize the power supply wire used (i.e., the overall length of the wiring to each sensor from the unit), as well as minimize the maximum distance from the central unit (which uses radio transmissions to receive broadcasts from the individual sensors). Formulate two linear programs to approximately solve the problem.