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 Noon-1:00 p.m. 9 1:00 p.m. -2:00 p.m. 9 2:00 p.m.-3:00p.m. 3 3:00 p.m.-4:00 p.m. 3 4:00 p.m.-5:00p.m. 3 5:00 p.m. -6:00 pm 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 30.1x, +30.1x2 + 30.1x3 + 30.4x4 + 30.1x5 + 30.1x6 +30.4xy + 30.4x7 s.t. 11:00 a.m. *. >8 (C) Assume that part-time employees can be assigned either a s-nour or a 4-nour snitt. Develop a minimum-cost schedule for the part-time employees. (Let x; be the same variabies from part a. Let y; - the number 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 X 1:00 pm X 2:00 p.m. X 3:00 p.m. x 4:00 p.m. X 5:00 p.m. X 6:00 p.m. X 7:00 p.m. X 8:00 p.m. X 9:00 p.m. X X 14 X2, X3, 44, 45, 46, 47, *gr 41Y21431 V4, Y. You Vy. Yg, Y20 Find the optimal solution. (*1, X2, X3, X2, X5, X6, 7, V1V2V3, 44, 45, Yer Y 7. Y gr 7g) = How many part-time shifts are needed, and what is the cost savings compared to the previous schedule