Assessment of the Impact of Costs on the Profit Optimization Model for the Sale of Services
The study carried out mathematical modeling of the profit optimization process when selling services with restrictions on the cost of services, the number of services sold. The gosl of the study was to construct a profit optimization target function based on the service sales history. The objectives of the study included the determination of optimization parameters, the development of numerical calculation methods, as well as conducting a numerical experiment to assess the impact of expenses on the optimal value of profit. The hypothesis of the study is to establish mathematical regularities between the main parameters of the financial process for the sale of services with the possibility of maximizing profits under restrictions on the cost and quantity of services. The research method was mathematical modeling, numerical solution of the nonlinear problem of finding the optimal solution using the Newton- Raphson method. An iterative scheme for calculating the optimal number of services sold is constructed. According to the results of the study, the proposed model will allow us to establish a functional pattern between the target function of profit and the cost of sales. The proposed model and numerical calculation methodology are of practical importance in order to increase financial income in the service sector. Within the framework of a numerical experiment, an assessment of the impact of costs relative to the critical cost of a service, at which there is no demand, on the change in the optimal values of the profit objective function and optimization parameters: the cost of a unit of service and the number of services sold.