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5. (-/20 points) DETAILS ASWMSCI15 4.E.025. MY NOTES ASK YOUR TEACHER 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 am 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 Number of Employees Needed 11:00 a.m.-Noon 9 Noon1:00 pm 9 9 3 3 3 1:00p.m.-2:00 pm 2:00 p.m.-3:00p.m. 3:00p.m. 4:00 pm 4:00p.m.-5:00p.m. 5:00p.m.-6:00 pm 6:00 p.m.-7:00 pm 7:00 pm-8:00p.m. 8:00 pm -9:00 pm 6 12 12 2 9:00 pm - 10:00 pm 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 / where I = 1 = 11:00 a.m., 1 = 2 = Noon, etc). Min work beginning at hour / where i = 1 = 11:00 a.m., 1 = 2 = Noon, etc). Min s.t. 11:00 am Noon 1:00 pm 2:00 pm 3:00 pm 4:00 pm 5:00 pm 6:00 pm 7:00 pm 8:00 pm 9:00 pm (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-hc This answer has not been graded yet. 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., 1 = 2 = Noon, etc). Min s. 11:00 am Noon 1:00 pm 2:00 pm 3:00 pm 4:00 pm 5:00 pm 6:00 pm 7:00 pm 8:00 pm 9:00 pm Xxx X2 X3 X4, X5, X6 Xy, *g. Y 14Y24V3, 74, 75, 76 77. YgYg 20 Find the optimal solution (X2, X2, X3, X4 X5 X6, Xy, Xg, Vi, V2, V3, 74, 75, 76, 77, Yg: 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 &