$[15$ points$]$ An assembly line with $30$ activities is to be balanced. The total amount of time to complete all $30$ activities is $60$ minutes. The longest activity takes $2\mathrm{.}4$ minutes and the shortest takes $3$ minutes. The line will operate for $480$ minutes per day. The line is balanced using $14$ workstations and a finished product can be produced every $4\mathrm{.}5$ minutes.

a$.$ What are the maximum and minimum cycle times?

b$.$ How much daily output will be achieved by each of those cycle times?

c$.$ What is the production rate in units per day?