Question

Problem 4-25 (Algorithmic)

Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 A.M. to 10:00 P.M. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average wage rate for the part-time employees is $7.9 per hour, but the temp agency managing the part time staff will charge the steakhouse one extra dollar per hour for shifts starting after 3:00 PM. The total number of full-time and part-time employees needed varies with the time of day as shown.

Time	Total Number of Employees Needed
11:00 a.m. - Noon	3
Noon - 1:00 p.m.	5
1:00 p.m. - 2:00 p.m.	6
2:00 p.m. - 3:00 p.m.	8
3:00 p.m. - 4:00 p.m.	9
4:00 p.m. - 5:00 p.m.	10
5:00 p.m. - 6:00 p.m.	11
6:00 p.m. - 7:00 p.m.	12
7:00 p.m. - 8:00 p.m.	7
8:00 p.m. - 9:00 p.m.	4
9:00 p.m. - 10:00 p.m.	4

One full-time employee comes on duty at 11:00 A.M., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 P.M. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern.

1. Develop a minimum-cost schedule for part-time employees. What is the total payroll for the part-time employees? If required, round your answer to the nearest dollar.
   
   Total daily salary cost = $  

   fill in the blank 1

   
   
   How many part-time shifts are needed?
   
   

   fill in the blank 2

   
   
   Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   

   
   
   

2. Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. If your answer is zero, enter "0".
   
   Optimal schedule for part-time employees:
   
   

   Starting Time	Number of part- time employees (4-hour shifts)	Number of part- time employees (3-hour shifts)
   11:00 A.M.	fill in the blank 4	fill in the blank 5
   12:00 P.M.	fill in the blank 6	fill in the blank 7
   1:00 P.M.	fill in the blank 8	fill in the blank 9
   2:00 P.M.	fill in the blank 10	fill in the blank 11
   3:00 P.M.	fill in the blank 12	fill in the blank 13
   4:00 P.M.	fill in the blank 14	fill in the blank 15
   5:00 P.M.	fill in the blank 16	fill in the blank 17
   6:00 P.M.	fill in the blank 18	fill in the blank 19
   7:00 P.M.	fill in the blank 20	fill in the blank 21

   
   How many part-time shifts are needed?
   
   

   fill in the blank 22

   
   
   What is the cost savings compared to the previous schedule? If required, round your answer to the nearest cent.
   
   Total cost reduced to $  

   fill in the blank 23

   .