1. (20 points) A license branch needs to arrange staff assignments so that customers are well-served. An analysis of past records shows that staffing...

1.  (20 points) A license branch needs to arrange staff assignments so that customers are well-served.  An analysis of past records shows that staffing on Fridays should be sufficient to handle 480 requests for title/license plate services, 230 requests for driver's license renewals/written tests, and 50 requests for road tests.  The license branch has three types of employees.  Road testers only do road tests, and each road tester can give 8 of them a day; they make $100 per day.  Clerks can handle both requests for title/license plate services (50 per day) and requests for driver's license renewals/written tests (24 per day); they make $80 per day.  Supervisors can handle both requests for title/license plate services (65 per day) and requests for driver's license renewals/written tests (28 per day); they make $120 per day.  There should be at least two supervisors working at all times.

A.  Write a linear program to find the least-cost staffing assignments for Friday.  Be sure to define your decision variables and label your constraints. (20 points)

Extra credit.  (10 points)  How many of each type of employee should the license branch have on Fridays?  Formulate a goal program to find the answer, given the prioritized goals listed below:

                P1:  Keep personnel costs below $1600.

                P2:  Provide service for at least 480 requests for title/license plate services.

                P3:  Provide service for at least 80 requests for road tests.

                P4:  Have 2 supervisors on duty--no more, no less.

                P5:  Provide service for at least 230 requests for driver’s license/ renewals /written test services. 

Explain how you would deal with the problem of normalizing.