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Adequate electric power generation depends on many factors which include: investment cost, fuel cost, maintenance cost, operation cost, number and capacity of generators. And because of the increasing demand for electric energy day in day out due to exponential increase in population, industries and organizations, there is need for optimal future planning in an attempt to meet the demand of the people. In this work, we present a linear programming model which based on integer formulation of electric power system generation in an attempt to optimally planning, minimize, and predict the future cost of generation. The model was solved using an iterative optimization method named ‘branch and bound’ and real life data was used for better understanding. The result obtained shows that the cost of generation can be minimized with maximum output and the future cost of generation can also be determined for optimal planning.