METHOD OF THE SOLUTION OF SOME CLASSES OPTIMISING TASKS
The relevance of this work is caused by wide circulation in all spheres of activity of important practical tasks which can be solved by methods of linear programming. The main difficulty at application of a universal way of the solution of such tasks (a simplex – a method) is its computing complexity. For the solution of this problem special methods of the solution of private problems of linear programming, for example, are developed for positive or limited basic data. These special cases are proved by economic, social, technical, technological sense. In this article the method maximizing linear function at one linear restriction with positive coefficients is developed. This method is generalized on a case of maximizing linear function at several linear restrictions. The received theoretical results are proved by the proof of the corresponding theorems. For an illustration of the received results numerical examples are given. The algorithmic complexity of the developed method is estimated for solvable tasks by calculation of number of the used operations and comparison with their quantity when using a simplex – a method. The received results allow to solve applied optimizing problems in various areas, including in problems of planning of production, a balanced diet and a diet, management of educational process, etc.
Keywords: a problem of linear programming, function, restriction, coefficient, a simplex – a method, an optimal solution.