A recipe for $10$ servings of fruit punch requires $3$ cups of orange juice, $1$ cup of pineapple juice, and $\frac{1}{4}$ cup of lime juice. A host has $10$ cups of orange juice, $3$ cups of pineapple juice, and $1$ cup of lime juice. If the host follows the recipe proportions, what is the greatest number of servings of fruit punch they can make?