The author analyzes, from the geometric viewpoint, the following {\it tolerance problem}:
Given:
the desired intervals ${\bf b}_i$ for the characteristics $b_i$ of the system; and
the intervals ${\bf a}_{ij}$ that describe the possible values of the coefficients $a_{ij}$ relating these characteristics and the design parameters $x_1,x_2,\ldots$: $b_i=\sum a_{ij}x_j$;
To describe:
the set of all designs $(x_1,x_2,\ldots)$ for which $b_i\in {\bf b}_i$ is guaranteed (i.e., for which for every $a_{ij}\in {\bf a}_{ij}$ the values $b_i$ are in the desired intervals ${\bf b}_i$).