A Florida juice company completes the preparation of its products by sterilizing, filling, and labeling bottles. Each case of orange juice requires \( 9 \) minutes (min) for sterilizing, \( 6 \) min for filling, and \( 1 \) min for labeling. Each case of grapefruit juice requires \( 10 \) min for sterilizing, \( 4 \) min for filling, and \( 2 \) min for labeling. Each case of tomato juice requires \( 12 \) min for sterilizing, \( 4 \) min for filling, and \( 1 \) min for labeling. If the company runs the sterilizing machine for 

\( 398 \) min, the filling machine for \( 164 \) min, and the labeling machine for \( 58 \) min, how many cases of each type of juice are prepared?