MUKACHEVO, Ukraine — Before gliding along trails or sliding down slopes, many of the world’s skis start at this bustling, sprawling factory in western Ukraine.

Here, skilled machinists combine wobbly ribbons of carbon fiber and thin sheets of stiff titanium, stacking them like cake layers, and then heat-pressing, shaping and polishing them into finished slats for cross-country or downhill use.

Here, too, craftworkers steam and bend wood into the sticks used by hockey players around the world under brand names that include Nike and Oxelo.

The factory’s Austrian owner, Fischer Sports, pays employees the equivalent of about $307 a month on average — perhaps one-eighth the amount that skilled woodworkers and machinists might earn in Fischer’s home country.