A large flower arrangement contains \(3\) types of flowers: carnations, lilies, and roses. Of all the flowers in the arrangement, \(\dfrac12\) are carnations, \(\dfrac13\) are lilies, and \(\dfrac16\) are roses. The total price of which of the \(3\) types of flowers in the arrangement is the greatest?

(1) The prices per flower for carnations, lilies, and roses are in the ratio \(1:3:4,\) respectively.
(2) The price of one rose is \(\$0.75\) more than the price of one carnation, and the price of one rose is \(\$0.25\) more than the price of one lily.

Answer: A

Source: Official Guide