We consider here a solvable task of optimizing purchases in Internet through the Center of network trade (CNT), that is yet absent (see Note below), of piece goods (PG), which are needed for a network user (online buyer) and for which he is ready to spend a pre-allocated amount of money. Attractiveness of each PG, that is of interest to the user, is specified via a weighting factor, which characterizes its usefulness. The result of solving this task is such set of PG, which belong to their initial set, when are fulfilled two conditions:

• their total cost does not exceed a specified amount of investment of a network user;
• the sum of utility values of these PG is highest among all possible variants of their choice.

Note. CNT will unite in itself those online stores that support the new perfect technology of online trade (i.e. trade in the Internet), that fully meets the interests of any network buyer. This technology of particular application has been proposed by the founder of IT AC DTIP (see below) and is based on the last one, having a lot of applications.

     This task can be solved numerically by using the new science-intensive network technology called "Information technology of automation of control of discrete technological and information processes (in short — IT AC DTIP)", because optimizable process has all necessary properties for that. This process is discrete and is classified as an instant process of selecting choices. Its elements in terms of DTIP are:

• PG of online stores, which are available for purchase through CNT, — demands;
• amount of investment of an online buyer — a device of service.