The electric power sector like any other sector provides services to the public with one of its aim as making profit; this ensure that human and material resources involve in running the business are well taken care of so as to keep the business on and improve on customer satisfaction. This can be achieved by maximizing profit without placing exorbitant tariff on customers. Hence, reducing the cost of running the system will be a source of maximizing profit. This paper shall consider how the running of the system can be reduced in the generation stage- reducing the total fuel burnt in generating a specific amount of power in the system per hour. This paper shall consider only part of the Nigeria electric power sector as a case study, precisely the Niger-Delta region of Nigeria. We shall assume that the power generated by the plants in the region is also consume there. Research shows that for a total power demand/generation of  by all generating units in the region, a total of  of fuel will be burn. But with the system of running cost minimization developed in this paper, about  of fuel will be burnt in generating that same quantity of power demanded resulting a net savings of .