Question $1.$ An assembly line with $8$ tasks is to be balanced. The longest task is $10$ minutes, and the total time for all tasks is $45$ minutes. The line will operate for $450$ minutes per day. Round up your answers to the nearest whole number $(40$ points, $10$ points each$).$ See Lecture M$4-2$ for details.

a$.$ What is the maximum output rates $($The most that can possibly be made in a day$)?$