$($Process Analysis$)$ Students are going through a three$-$step process to obtain their ID cards from the ID card center. Each student will spend $2$ minutes at the registration desk before going to one of three cashiers to pay a fee for the card. After that, he$/$she will visit one of four ID processing stations to have his$/$her picture taken and the ID card printed. Visits to the cashier and ID processing station take $10$ and $20$ minutes respectively. The demand rate is $30$ students per hour.

a$.$ What is the capacity $($in students per hour$)$ of each step?

b$.$ Which step is the bottleneck?

c$.$ What is the process capacity $($in students per hour$)$ of the ID card center?

d$.$ What is the flow rate $($in students per hour$)$ of the ID card center?

e$.$ Is it capacity$-$constrained or demand$-$constrained?

f$.$ What is the cycle time $($in minutes$)$ of the ID card center?

g$.$ What is the utilization of each step?