To obtain your first driver’s license, you must successfully complete several activities. First, you must produce the appropriate identification. Then, you must pass a written exam. Finally, you must pass the road exam. At each of these steps, 10 percent, 15 percent, and 40 percent of driver’s license hopefuls fail to fulfill the step’s requirements. You are only allowed to take the written exam if your identification is approved, and you are only allowed to take the road test if you have passed the written exam. 

Each step takes 5, 3, and 20 minutes, respectively (staff members administering written exams need only set up the applicant at a computer). Currently, the DMV staffs 4 people to process license applications, 2 to administer written exams, and 15 to judge the road exam. DMV staff work 8 hours per day. 

(a) Where is the bottleneck, according to the current staffing plan? 

(b) What is the capacity of the process (expressed in approved cases per day)?