Answer Happy

A linear programming computer package is needed. 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 $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown. Time 11:00 a.m.-Noon Noon-1:00 p.m. 1:00 p.m.-2:00 p.m. 2:00 p.m.-3:00 p.m. 3:00 p.m.-4:00p.m. 4:00 p.m.-5:00 p.m. 5:00 p.m.-6:00 p.m. 6:00 p.m.-7:00 p.m. 7:00 p.m.-8:00p.m. 8:00 p.m.-9:00 p.m. 9:00 p.m.-10:00 p.m. Number of Employees Needed 9 9 9 3 3 3 6 12 12 7 7
(a) Develop a minimum-cost schedule for part-time employees. (Let x, the number of part-time employees who start work = beginning at hour / where/= 1 = 11:00 a.m., /=2= Noon, etc). Min 5.t. 11:00 a.m. 30.4x Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. x 9:00 p.m. X1 X2 X3 X4 X5 X6 X7, X8 20 Find the optimal solution. (X₁ X₂ X3
(b) What is the total payroll (in $) for the part-time employees? $ 608 How many part-time shifts are needed? 7 x shifts Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts.
(c) 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. (Let x, be the same variables from part a. Let y, the number of part-time employees who start work beginning at hour / where/= 1 = 11:00 a.m., / 2= Noon, etc). Min. s.t. 11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. X1 X2 X3 X4 X5 X6X7 Find the optimal solution.. (X₂ X₂ X3 vY2 Y2 Y3 Yar YS: Yo Y7 Yg. Yg) =([ How many part-time shifts are needed, and what is the cost savings compared to the previous schedule? part-time shifts needed cost savings S Yar 20 Y7 YBY 20