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 $7.50 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 Noon1:00 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.-4:00 p.m. 3 4:00 p.m.-5:00 p.m. 3 5:00 p.m.-6:00 p.m. 6 6:00 p.m.-7:00 p.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. X 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, X, X, X4, Xg, Xq, X, X 20 Find the optimal solution. (Xq: X2 X 4' Gr *, *) = (b) What is the total payroll (in $) for the part-time employees? $ How many part-time shifts are needed? shifts x (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 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. 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, X, X, X 1 X gr X gr Xq, X gr Yar Yar Y r Y 4 Y g Yer Y q, Y gr Yg 20 Find the optimal solution. (x,y Xpy, X3Xqr Xsy Xp, Xy, Xp. Y?! Yz. Yz, Yar Ys Y61 YyYgYg) -( D How many part-time shifts are needed, and what is the cost savings compared to the previous schedule? part-time shifts needed cost savings $