One important and challenging problem for sensor network is how to ensure coverage of the target area and maximize the lifetime of the network at the same time. This problem is known to be a NP-complete and there are many attempts to find an approximate solution. In this paper, we reduce the problem of area coverage to target coverage and it is possible to compute an upper bound on the lifetime achievable for target coverage. We have given an Integer Programming Problem (IPP) formulation of the problem using this upper bound. We do some approximation on the problem before applying IPP, so that solution could be obtained in reasonable time. In the experiments with number of sensors ranging from 50 to 150 we have been able to achieve the upper bound in all the cases.