An object tracking sensor network (OTSN) is made of m static wireless sensors scattered throughout a geographical area for tracking n mobile targets. Assuming that sensors have non-rechargeable batteries, one of the most critical aspects of OTSN is energy consumption. In this paper, we propose linear programming models which handle two missions: monitoring and reporting data to a base station, and two distinct problems : minimize energy consumption and maximize network lifetime. We suppose that trajectories of targets are known and targets should be monitored by sensors. To reach our goals, we schedule the active and sleep states of the sensors and route the data to a base station while keeping track of the targets. To solve our problems, we process a temporal discretization according to the intersection points between the trajectories and the sensing ranges of the sensors. The obtained sets of sensors for each time window help us to create linear programming models. These basic problems offer perspectives in performance evaluation of energy-conservation protocols and distributed algorithms in wireless sensor networks.