Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned. However, there are numerous forms of them existing in lower and higher orders of the classical method. This work investigates the linear stabilities and abilities of some selected explicit members of these Runge-Kutta methods in integrating the singular Lane-Emden differential equations. The results obtained established the ability of the classical Runge-Kutta method and why is mostly used in computations.

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.