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In Ghana, the majority of reliable electricity is generated in centralized plants. This type of electricity generation structure undoubtedly contributes to the economic rise in electricity tariffs and transmission losses due to the operational cost of such plants and their vast distances from the communities respectively. In this paper, Linear Programming was used to nd the optimal power dispatch of a decentralized grid-connected photovoltaic system in the form of a microgrid for a minimum cost of electricity. The fundamental LP problem was optimized in AMPL (A Modeling Language for Mathematical Programming) properly employing the CPLEX solver. In the case study, the involvement of microgrid in the energy sector convincingly demonstrated a daily cost of GHS63,426.23 in the rst ve years accurately representing 18% potential reduction. This cost reduction will be increased tremendously to 75% in subsequent years. This is a lower energy bill as compared to the bill of the existing electricity structure.