In real world situations,we use optimization techniques to obtain optimal solu tions. Resources are scarce and we seek to utilize them, maximizing the profits obtained while minimizing the time and cost associated with them. Linear pro gramming is one of many optimization techniques. It is the simplest technique as it enables solving complex optimization problems by making few simplified as sumptions. In this research paper,we will focus on a transportation problem,and an assignment problem which are linear programming problems. Different situ ations give rise to the assignment problem, where we must discover an optimal way to allocate n resources to m facilities. We will use the Hungarian method in solving the assignment problem. Computations for both linear programming problems will be done in a statistical software known as R, using the packages lpSolve and lpSolveAPI. In the case of the transportation problem, we seek to minimize the costs associated in transporting petroleum from refineries A,B and C to four petrol stations 1,2,3 and 4. For the assignment problem, we allocate 4 persons;A,B,C and D to different tasks 1,2,3 and 4 such that the total cost is minimized.