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 fulfil 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 toe 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 to set up the applicant at a computer). Currently the DMV staffs 4 people to process the license applications, 2 to administer the written exams and 5 to judge the road exam. DMV staff are rostered to work 8 hours per day.

How many staff should the DMV roster at each step if it has a target to produce 100 newly-licensed drivers per day while maintaining an average staff utilisation factor of 85%? Show your workings.