Sprinkle yeast over warm water and let dissolve for five minutes. Put milk and shortening in a small sauce pan and warm until shortening melts. Cool to lukewarm. Pour yeast mixture into a mixing bowl; add milk mixture and 2 cups flour. Beat briskly until well mixed. Add remaining flour and mix well. Cover the bowl and let rise in a warm place until doubled in size. Turn dough out onto floured surface. Dough will be soft but managable. Pat the dough into a circle about 1/2 inch thick. Cut doughnuts out with a three inch doughnut cutter. Place doughnuts on a greased baking sheet and let rise, uncovered for about 20 minutes. (Doughnuts do not spread much, you can place them about 1 inch apart on baking sheet). Preheat oven to 450 deg f. Bake about 10 minutes or until lightly golden. Remove from oven and brush with melted butter. Sprinkle with cinnamon and sugar mix. Variation:Instead of cinnamon-sugar mix, let doughnuts cool after brushing with butter. When cool dip in glaze made with powdered sugar and milk. Makes about 30 doughnuts. Each doughnut = 125 cal, 3.9 g fat. (28.5 % calories from fat).