Question

The local Department of Motor Vehicles (DMV) issues new licenses and renews licenses. (See the diagram below.) 48 applicants enter the DMV per hour. All applicants see the receptionist first. The receptionist directs them in one of three directions: 75% of the applicants are sent directly to the issue-license Station where a new photo and license are done. 10% of the applicants must first take a multiple-choice test on one of the computers. The remaining 15% of applicants should first take an eye-exam. Only 80% of the applicants who take the eye exam pass the exam. The remaining leave. The applicants who pass the eye exam are also directed to the multiple-choice computer test. Out of all the applicants who take the multiple-choice test (coming either directly through the receptionist or after the eye exam), 5% fail it. The rest who pass the multiple-choice test proceed to the issue-license section. Get a piece of paper, draw the diagram clearly and carefully, and add the flows. The number of workers and workload are given below.

Activity Reception	number of workers (c) 1	Activity time (Tp) in mins. 0.4
Eye-Exam	1	5
Comp-Test	3	15
Issue-License	12	6

Compute the Capacity of this system. The potential answers are:

A: 25.57 applicants per hour. B: 54.55 applicants per hour. C: 27.78 applicants per hour. D: 50 applicants per hour. E: 20.71 applicants per hour.

Answer 1

Max output of reception = 60/0.4 = 150 per hour

Max output of eye exam = 60/5 =12 per hour

Max output of comp test = 3x60/15 = 12 per hour

Max output of Issue license = 12 x 60/6 =120 per hour

Number of persons visiting at reception =48

Numebers visiting eye exam =0.15x48 =7.2

Numbers visting computer test = 0.1x48+7.2x0.8 =10.56

Numbers visiting issue license = 48x0.75+10.56x0.95 =46

It can be seent hat the bottleneck is computer test which is the slowest station.

If maximum customers which can be handled is N ( the number which will lead to 100% utilisation of this station) . then

0.1xN +0.15x0.8xN =12

N=12/0.22 =54.55

B is right option.

WOICE Reception issue Comp. Test Trease Eye Exam