Charles and Madeline run an event management business in which they have two major tasks: getting new clients and preparing food for the events. Charles takes $6$ hours to prepare food for an event and $3$ hours to get each new client. Madeline takes $12$ hours to prepare food and $3$ hours to get a new client. Charles and Madeline were initially splitting both tasks for a large number of events. However, they later decide to start reassigning work based on the principle of comparative advantage. Charles takes over food preparation while Madeline uses the free time to get more clients. Which of the following is a possible effect of specialization on the tasks performed by Charles and Madeline?

a$.$ The total number of events for which food is prepared will remain unchanged, but the number of new clients will increase by $2.$

b$.$ The total number of events for which food is prepared will increase by $3,$ and the number of new clients will increase by $1.$

c$.$ The total number of events for which food is prepared and the number of clients will remain unchanged.

d$.$ The total number of events for which food is prepared and the number of new clients will increase by $2.$