Problem 6: (Restaurant work scheduling problem).

The famous Chang's Restaurant is open 24 hours a day.

Waiters and busboys report for duty at 3 A.M., 7 A.M., 11

A.M., 3 P.M., 7 P.M., or 11 P.M., and each works an 8-

hour shift. The following table shows the minimum number

of workers needed during the six periods into which the

day is divided. All workers get paid $14 per hour. The

people starting at 11 PM and 3 AM also get an extra $3

per hour as night shift differential. Chang's scheduling

problem is to determine how many workers should report

for work in each shift to minimize the total staff cost for one

day's operation.

a. Formulate an LP model for this problem. (Define the

decision variables, show the objective function, and

list each constraint algebraically.)

b. Solve this LP problem. What is the optimal solution

and the value of the objective function?

c. How much surplus manpower is there in each work

period?

d. If it is possible to hire part-timers to work from 11AM to

3 PM and again from 7 PM to 11 PM at a cost of $20

per hour, what will be optimum solution?