All processes take time to complete. While physical processes such as acceleration and deceleration take little time compared to the times need to travel most distances, the times involved in biological processes such as gestation and maturation can be substantial when compared to the data-collection times in most population studies. Therefore, it is often imperative to explicitly incorporate these process times in mathematical models of population dynamics. These process times are often called delay times, and the model that incorporate such delay times are referred as delay differential equation (DDE) models. The models will examine some theoretical concepts and their applications to real life situation. The application examines measles and the time it takes to manifest or to its removal or treatment from the system. The solutions of the models will be displayed in graphical forms using MATLAB method. The analysis of the models indicate the times delay and its characteristics.

Graph coloring is an important aspect of graph theory with great application in University timetable scheduling. The examination timetable scheduling maximizes the time and minimizes resources (venue and invigilators) to give effective output of the event. The constraint based approach method is implemented in scheduling examination timetable for Faculty of Science, Federal University Lokoja. Then the results on thirteen (13) departments give a 3-timeslot within twelve (12) days examination period with no students having two (2) examinations per day. In all, there is no conflict of venues and courses thereby giving an efficient scheduling process for the entire examination.

Linear programming is applied to bread production and the raw materials for the research were collected from the bakery industry in Lokoja which were clearly identified. The paper took into account three types of bread with estimated profits and the problem was formulated from the collected data. The formulated problem was parameterized into parametric linear programming and run using the developed algorithm of linear programming The result obtained indicates that profit is made at d different values of the parameter,t, leaving the company the choice of any profit it wants to get.

This paper critically examines parametric linear programming problem (PLPP) with interval in the coefficients of the objective function and the composition of Plus, Beauty and Nova soap. The finding of soap production in NASCO Company in Jos, Nigeria will be studied and the problem formulated. The formulated problem is tested using the developed computer program by varying the parameter at regular interval and obtaining the corresponding values of the objective function. The interpretation of the results will be analysized.