A fruit punch recipe yields $8$ servings and requires $2$ cups of orange juice, $1.5$ cups of pineapple juice, and $0.5$ cup of grenadine. Michael wants to make this punch and has $5$ cups of orange juice, $6$ cups of pineapple juice, and $1.5$ cups of grenadine. Assuming he uses all available ingredients optimally while maintaining the recipe's ratios, what is the maximum number of servings he can prepare?