R is one of the widely used statistical software that analyse varying amounts of data and execute both simple and complex commands dealing with different data types. Optimx is one of the over 8000 packages and is used in R to help in the computation of optimization problem. In order to start using Optimx one downloads it from CRAN website and loads it into R alongside its subsets such as optim and quadprog. The purpose of this research is to show how to apply concepts of mathematical optimization on solving real life problems. In this project we try to solve vendor’s problem on how many units of banana that will yield maximum profits using optimization.The first section introduces the problem and how we endeavour to solve it. We also discuss and analyse our results in the last two sections. The anticipated outcome of this research is to incorporate the use of optimization techniques in solving problems in the business sector. This information is likely to impact on the level of income by both small scale and large scale businesses.