2. Statement of the solvable task

     Here we use the following notations:

  • GSgoods and services;
  • AGalternative groups of GS;
  • NG — a non-alternative such group.


  • amount of a family budget, which is allocated for future acquisitions of the most important GS for the family members;
  • one of two possible criteria of usefulness for GS, which are selected for their acquisition:
    • utility ratio for a sample of GS (relative criterion);
    • purchasing worth of a sample, that is equal to the product of its utility ratio by its cost (absolute criterion);
  • a set of available for acquisition GS, which are divided into several categories and are of practical interest for the family members (boots, fur coats, cars, computers, package tours to sea, subscriptions to sport centers, etc.);
  • for each such category are given the number of GS, for each of them are set:
    • name and description of a GS sample;
    • its cost;
  • formed by investor (a head of family) several AG for GS, selected by him, and one NG;
  • for each chosen GS is given a value of criterion of its sample usefulness;
  • for each AG are set the minimum and maximum numbers of acquired samples of various GS, included in this group;
  • for each GS of a single NG are set the minimum and maximum numbers of its acquired samples.

     Maximized quality criterion: total purchasing worth of acquired GS under given restriction on the value of a family budget.