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.