please be specific and organized with the answers

(a) Develop a minimum-cost schedule for part-time employees. (Let xj= the number of part-time employees who start work beginning at hour where i=1=11:00 a.m., l=2= Noon, etc). \begin{tabular}{l} Min \\ s.t. \\ 11:00 a.m. \\ Noon \\ 1:00 p.m. \\ 2:00 p.m. \\ 3:00 p.m. \\ 4:00 p.m. \\ \hline 8:m. \\ \hline 6:00 p.m. \end{tabular} 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. x1,x2,x3,x4,x5,x64,x7,x80 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. 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 xj= the number of part-time employees who start work beginning at hour i where l=1=11:00am,,l=2 = Noon, etc). 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8,y90 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. x1,x2,x3,x4,x5,x6,x7,x8,y1,y2,y3,y4,y5,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 (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 xi be the same variables from part a. Let yi= the number of part-time employees who start work beginning at hour / where i=1=11:00 a.m., i=2 = Noon, etc). Min s.t. 11:00 a.m. 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. 8:00 p.m. 9:00 p.m. x1,x2,x3,x4,x5,x6,x7,x80 Find the optimal solution. (x1,x2,x3,x4,x5,x6,x7,x8)=( (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 employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. (Let xj be the same variables from part a. Let yj= the number of part-time employees who start work beginning at hour i where l=1=11:00 a.m., l=2 = Noon, etc). Min s.t