A linear programming computer package is needed. 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. 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 xf= the number of part-time employees who start work beginning at hour i where i=1=11:00a.m1,i=2= Noon, etc ). Min s.t. 11:00 a.m. Noon 1:00p.m. 2:00p.m. 3:00p.m. 4:00p.m. 5:00p.m. 6:00p.m. 7:00p.m. 8:00p.m. 9:00p.m. x1,x2,x3,x4,x5,x6,x7,x80 Find the optimal solution. (x1,x2,x3,x4,x5,x6,x7,x8)=( 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 =) 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 xi be the same variables from part a. Let y1= 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 1:00p.m. 2:00p.m. 3:00p.m. 4:00p.m. 5:00p.m. 6:00p.m. 7:00p.m. 8:00p.m. 9:00p.m. x1,x2,x3r,x4,x5,x6,x7,x8,y1,y2,y3,y4,y52,y6,y7,y8,y90 Find the optimal solution. (x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8,y9)=() 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