The Applications of linear programming are so diverse and in wide used by business, industries, and organisations in advance econimies. However, the extent to which Nigerian businesses are utilising the many opportunities provided by linear programming models is anything but encouraging. This research work surveys the present position of oil company attempting to maximise its profit. A critical examination of its current distribution method has been made and an alternative method offered as a better alternative because it is cost effective and is based on a simple, basic scientific method rather than rule of thumb or intuition. Specifically attempt is made to show the benefit to be derived in using transportation model. The study achieves this by illustrating the mechanics of the transportation model, and lays foundation for further inquiry into potentially profitable applications of the various techniques of linear programming.