Alinear 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. Min 11:00 am-Noon Noon-1:00p.m 1:00p.m.-2:00p.m. 2:00 pm-3:00p.m. 3:00p.m.-4:00p.m. 4:00 pm-5:00p.m. 5:00 pm-6:00p.m. 6:00 pm-7:00p.m. 7:00 pm-8:00p.m. 8:00p.m.-9:00p.m &.L. 11:00 am Noon 1:00 pm 2:00p.m. 3:00p.m. 4:00p.m. 5:00p.m. 6:00 pm. 7:00p.m. Min 8:00 pm. 9:00 pm-10:00p.m. One full-time employee comes on duty at 11:00 am, 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/where /-1-11:00 a.m.,/-2-Noon, etc). 9:00 pm. ₂₂ 20 Find the optimal solution. Wyyyy x₂ - ( This answer has not been graded t Time 11:00a.m. Noon 1:00p.m. 2:00p.m. 3:00p.m. 4:00p.m. 5:00 pm. 6:00 pm. (b) What is the total payroll (in $) for the part-time employees? $ How many part-time shifts are needed? 7:00 pm. Number of Employees Needed Use the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts. 8:00p.m. 9 9:00 pm. 9 9 (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 am,/-2-Noon, etc). 3 3 3 $ 6 12 12 7 7 XyX² ₂² ₂² ¥ y Y q ¥g Yg Yy Yg Y Z 0 ** Find the optimal solution. * * * * * * * *۰ ۰ ۰ ۰ ۰ ۰ gr 12 - ۷۷۰ ۷۶ ۷۷ ۷) - ( How many part-time shifts are needed, and what is the cost savings (in $) compared to the previous schedule? part-time shifts needed cost savings