The Leontief input-output model describes the inter-industry relationships with linear algebraic tools. The productivity of economics is expressed in terms of the Perron eigenvalue of the consumption matrix. Suppose for each sector of economics, we have several types of technologies to organize production. We need to make a choice for each sector to make the whole economics productive. Mathematically, this is equivalent to minimizing  the spectral radius over a special set of nonnegative matrices. This problem is notoriuosly hard. Nevertheless, in most cases it can be efficiently solved by the so-called spectral simplex method. Some interesting relations of this problem to other areas of mathematics such as combinatorics and functional analysis will also be discussed.