A recipe for $5$ servings of a mixed berry smoothie calls for $1.5$ cups of yogurt, $1$ cup of mixed berries, and $0.5$ cup of apple juice. A chef has $4$ cups of yogurt, $3$ cups of mixed berries, and $1.25$ cups of apple juice. If the chef follows the recipe proportions, what is the greatest number of servings of smoothie they can make?