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 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 Number of Employees Needed 11:00 a.m.-Noon 9 Noon-1:00 p.m. 9 1:00 p.m.-2:00 p.m. 9 2:00 p.m.-3:00 p.m. 3 3:00 p.m.-4:00p.m. 3 4:00 p.m.-5:00 p.m. 3 5:00 p.m.-6:00 p.m. 6 6:00 p.m.-7:00p.m. 12 7:00 p.m.-8:00 p.m. 12 8:00 p.m.-9:00 p.m. 7 9:00 p.m.-10:00 p.m. 7 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. (a) Develop a minimum-cost schedule for part-time employees. (Let x = the number of part-time employees who start work beginning at hour i where i = 1 = 11:00 a.m., i = 2 = Noon, etc). Min s.t. 11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. *1 X, 20 Find the optimal solution. (X1, X2, X3, X4, X5, X5, X7, xg) = (b) What is the total payroll (in $) for the part-time employees? How many part-time shifts are needed? 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 i wh i = 1 = 11:00 a.m., i = 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. Xq, X2, X3, X4, X5, X5, X7, Xgo V 11 V 21 31 V 41 V 51 V 51 V 7. YgV20 Find the optimal solution. (Xq, X2, X3, X4, X5, X5, X5, Xg, V1, V2, V3, V4, V5, VS, Y 7, V, Vo) = How many part-time shifts are needed, and what is the cost savings compared to the previous schedule? part-time shifts needed cost savings $