Journal of Applied & Computational Mathematics

In this paper, a two stage production inventory model for non-deteriorating items with a constant demand rate and completely backlogged is presented. The production rate of the model is assumed to be a constant and to be proportional to demand rate. Each cycle time of the developed model is partitioned in four different time stages. The optimum total inventory cost per cycle and the optimum time for each stage are determined. The proposed model is illustrated with a numerical example and it has been analyzed sensitively with respect to each one of its parameters.

Changes in the ratios of married people, adulterers, and divorcees are explained by the creation of a mathematical model in this paper. Using the equations expressing the proportions of adulterers and divorcees, a formula was created to predict the percentage of couples in the country who use the inversion transformation. Two threshold conditions were revealed by the qualitative study: The fundamental reproductive numbers for an adulterer and a divorcee in a married setting. A divorcee persuades a spouse to dissolve their marriage on average every year, according to these threshold conditions. However, the instability of the divorce-adultery equilibrium point indicates that a significant proportion of couples were either divorcing or committing adultery. A couple may occasionally sleep apart for five or six days each month outside of their union. The sensitivity analysis revealed that the rate at which spouses end their relationships when influenced by others is the primary cause of the country's growing divorce problem. However, the rate at which an adulterer divorces their spouse has a significant impact on the country's adultery prevalence.