An assembly line with $17$ tasks is to be balanced. The longest task is $2\mathrm{.}4$ minutes, and the total time for all tasks is $18$ minutes. The line will operate for $450$ minutes per day. $$ LO$5$

a$.$ What is the minimum number of workstations needed if the output rate is to be $180$ units per day?

b$.$ What cycle time will provide an output rate of $125$ units per day?

c$.$ What output will result if the cycle time is $($i$)9$ minutes?

$($ii$)15$ minutes?