The research results develop the ideas of environmentally safe technologies for waste processing, in particular the idea of mechanical processing of plastic waste and the mechanical isolation method of household and industrial waste disposal. The proposed technology makes it possible to process waste into construction products, as a final product – shell plastic containers filled with pressed waste. The patented design of the container consists of the lower part of the glass-shaped case, and the upper part – a lid hermetically attached to the upper end of the glass. This container can be made as a truncated polyhedral regular pyramid, which has at least three faces; the angle of apothem inclination of the truncated polyhedral regular pyramid to its vertical axis is chosen from the ratio 5 ≤ α ≤ 40. In addition, the container has a given volume by minimum surface area. The paper investigates the problem of constrained optimization with finding the values of the height and sides of the bases of a regular n-gonal truncated pyramid, for which the smallest value of the surface area is achieved, if its volume and the angle of inclination of the apothem to the vertical axis are known. For the analytical solution of this problem, the method of Lagrange multipliers is used, which reduces this problem to finding the solution of a system of three nonlinear equations with three unknowns.