In recent years, Nigeria has witness rapid development especially in the area of infrastructural development like roads, bridges, buildings etc. The conventional methods used in concrete mixing have its own peculiar problems, like time wasting, material wasting and errors. These problems have been the cause of structural failures which has given rise to loss of life and properties. Hence the need to development a method that will take care of all these anomalies witness in the conventional method. This work is aim at removing these anomalies by the use of Scheffes Optimization method. This optimization method can predict the compressive strength of a concrete given the mix ratios and also predict the mix ratios required to give a compressive strength for a particular concrete made by completely replacing river sand with quarry dust. With this method it will be easy to predict the compressive strength of concrete based on the type of structure it is to be used for, there by eliminating the problems associated with structural collapse due to errors in concrete mixing by conventional method.