Phasor Measurement Units (PMUs) are being considered as the essential tools in modern power system studies. In this paper a general approach is proposed to place the PMUs optimally in a power system and minimize the total installation cost to make the entire system completely observable. In this paper, the placement of PMUs is performed with respect to the maximum measurement redundancy, considering both cases of single PMU loss or single branch outages as just one problem. The proposed approach employs Binary Integer Linear Programming (BILP) to formulate the objective function. In order to consider more practical assumptions, with and without considering of zero injections buses, this method does not utilize the existing conventional measurement units in the power network. In addition, to show the effect of unequal PMU installation in each bus, modified cost matrix is added to the problem. The proposed approach is then applied to several standard IEEE test systems (14-bus, 30-bus and 57-bus) to find the optimal placement of the PMUs. The simulation results approve the capability of the proposed method in finding the optimal place of the PMUs with minimizing the installation cost.