The metal parts for a scooter are manufactured in two steps:

Step $1$: Metal stamping

Step $2$: Assembly

Each scooter is made up of the following metal components:

part A $3$ pieces

part B $1$ pieces

All of the parts are fabricated with a single stamping machine. A set$-$up time of $46$ minutes is required when switching between part types.

Once the machine is set up$,$ the activity time for parts is:

part A $-0\mathrm{.}16$ minutes per piece

part B $-0\mathrm{.}38$ minutes per piece

At assembly, all of the necessary parts from stamping, plus a number of small purchased components, are assembled manually to form the finished products.

Each scooter requires $82$ minutes of labor time to assemble. There are $36$ workers in assembly.

Assume there is sufficient demand to sell every scooter the system can make.