This paper presents a linear programming based solution for an Optimal Placement of Phasor Measurement Units (PMU) problem (OPP) under contingency situations. With the increasing usage of synchrophasors or PMUs for smart grid monitoring and control, the problem of PMU placement has become a major concern due to high installation costs. This paper uses a Linear Programming (ILP) approach to find optimal solutions. This paper shows that performance of the LP constraints and formulation makes the approach very attractive for smaller utilities with limited budgets. This is investigated with and without zero injection cases in the CPLEX solver. This paper also proposes an index called the Optimal Redundancy Criteria (ORC) that assists utilities in providing redundant observability for critical buses in the system. The proposed approach yields optimal solutions for full and redundant observabilities within 15 milliseconds (ms) for test bed cases such as the IEEE 14, 30, 57, 118, and 300 bus systems, and a 208 bus Southern region Indian power grid (SRIPG).