With a name like Inspiration Kitchen, you might think the poor and homeless go there to eat. But they go there to work. Cook County Board President Toni Preckwinkle saw it herself Friday during a visit to the West Side restaurant where residents who struggle with homelessness and poverty prepare meals for paying customers. The restaurant, 3504 W. Lake St., is part of Inspiration Corp., an organization founded in 1989 as Inspiration Cafe to give restaurant skills training to the poor and homeless. Today, the …