A cookie recipe yields $12$ cookies and requires $1.5$ cups of flour, $0.5$ cup of sugar, and $0.25$ cup of butter. Sarah wants to bake these cookies and has $6$ cups of flour, $2.5$ cups of sugar, and $1$ cup of butter. Assuming she uses all available ingredients optimally while maintaining the recipe's ratios, what is the maximum number of cookies she can prepare?