Selection of media and budget allocation is a major concern in advertising. It involves choosing the appropriate media that is effective in reaching the target audience of the population in consideration. Generally, predicting an optimal target audience exposure in selection of media is a complex problem. In this study, a Linear Programming technique is used to investigate the budgetary allocation of a Company for effective media selection planning. The problem is formulated using empirical data from the company and other media sources. The resulting linear programming model is analyzed using Quantitative Manager for Business version 3.2 and Linear Programming Solver version 5.2.2 which embodies the simplex algorithm method. The results show that the optimal target audience is 635,048,700. The optimum media mix which attracts a significant audience exposure and generates the desired objective value for the advertising campaign include; three (3) Television media outlet, two (2) print media outlet, and ten (10) radio media outlet.
This paper aims to study fuzzy multi-objective assignment (F-MOAS) problem. The problem is considered by incorporating trapezoidal fuzzy numbers. Through the α- level sets, the problem under consideration is converted into the corresponding ( α- MOAS). An interactive approach to improve the weights in the Weighted Tchebysheff program is suggested. Then the stability set of the first kind without differentiability corresponding to the resulted solution is determined. A numerical example is given for illustration.
We construct exponential objects in categories of generalized uniform hypergraphs and use embeddings induced by nerve-realization adjunctions to show why conventional categories of graphs and hypergraphs do not have exponential objects.
In this paper, we propose a SEIR-SEI epidemic model for malaria transmission which describes the interaction between human and mosquito population, with the effects of antibodies produced by the incidence rates for humans and mosquitoes respectively and two optimal controls. We introduce an optimal problem with an objective function, where two control functions, use of treated bed-nets and control effort on malaria treatment, have been used as control measures for infected individuals. The existence of feasible region where the model is well-known is established. Stability analysis of the disease -free equilibrium is investigated. The basic reproduction number R0; is obtained using the next generation matrix approach. The existence of the endemic equilibrium is also specified under certain conditions. Numerical simulations are carried out to confirm our analytic results and our simulation also suggests that, two control strategies are more effective than only one control in controlling the increase of number of infected individuals in the Democratic Republic of the Congo (DRC).
In this paper, a deterministic mathematical model incorporating interference is developed and analysed to investigate the role of interference on the transmission dynamics and management of HIV and AIDS. The model is shown to be positively invariant as well as bounded. The endemic state is shown to exist provided that the reproduction number is greater than unity. Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, the endemic states are shown to be locally and globally asymptotically stable. This implies that disease transmission levels can be kept quite low or manageable with minimal deaths at the peak times of the re-occurrences. Numerical simulations indicate that minimal interference against the disease lowers the rate of infection and enhances the disease management.