Additional Algo $5-9$ Flow$-$Dependent Processing Times

North Liberty Dental Associates has three different types of patients:

Type $1$ Patients $-$ Routine cleaning and exam

Type $2$ Patients $-$ Routine cleaning and exam with $x-$ray

Type $3$ Patients $-$ Filling

All patients need to check in and out with the front desk. The table below shows how many patients are expected per day and the number of minutes it takes each resource to deal with them.

$\backslash$table$[[,$Cases,Front Desk$],[$Type $1$ Patients $-$ Routine cleaning and,per Day,Person,Dentist Hygienist$/$Assistant$,,,],[$exam$,42,5,7,20,,],[$Type $2$ Patients $-$ Routine cleaning and,,,,,,$],[$exam with X$-$ray,$15,6,8,25,,],[$Type $3$ Patients $-$ Filling,$12,6,21,26,,]]$

North Liberty Dental has $1$ front desk person, $2$ dentists, and $4$ hygienist$/$assistant$.$ Each person works $8$ hours per day.

a$.$ What is the implied utilization of each resource?

Note: Round your answers to $3$ decimal places.

$\backslash$table$[[$Resource$,\backslash$table$[[$Implied$],[$Utilization$]]],[$Front Desk,$],[$Dentist$,],[$Hygienist$/$Assistant$,]]$

b$.$ Which resource is the bottle neck?

Which station is the bottle neck?