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 shirts during peak meal times. On Saturdays the steakhouse is open from 11:00 a.m. to 10:00p.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 Noon-1:00 p.m. 9 1:00 p.m.-2:00 pm 9 2:00 p.m.-3:00p.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. -8:00p.m. 12 8:00 p.m.-9:00 p.m. 7 9:00 pm - 10:00 pm 7 -hours-on, 1-hour-off, 4-hours- 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 work at 1:00 p.m. and works the same on pattern. (a) Develop 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. 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, X6, Xy, Xg 0 Find the optimal solution. (X2, X2, X3, Xps Xg, xe, xy, xz) = ( 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 employers 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 a.m., 1 - 2 - Noon, etc). Min s.t. 11:00a.m. Noon 1:00 pm 2:00 pm 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00p.m. 7:00 p.m 8:00 pm 9:00 p.m. *1,*2, 3, *4*5*5*, *3r 41 721 Y3. Yo Yo Yo Yo Yo Yo 20 Find the optimal solution. (X. X, X3, X4, 45, 46, 47, 48, 41. Vy. VzY4Y5 Ygyz. V. Yo) =( How many part-time shifts are needed, and what is the cost savings compared to the previous schedule? part-time shirts needed cost savings