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 $7.60 per hour. The total number of fulltime 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 x= the number of part-time employees who start work beginning at hour ( where i=1=11:00a.m1,i=2= Noon, etc). Min30.4x1+30.4x2+30.4x3+30.4x4+30.4x5+30.4x6+30.4x7+30.4x8 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 x1= the number of part-time employees who start work beginning at hour i where l=1=11:00am.,f=2= Noon, etc). Min30.4x1+30.4x2+30.4x3+30.4x4+30.4x5+30.4x6+30.4x7+30.4x8 s.t.11:00a.m. 3:00p.m.4:00pm.5:00p.m.6:00pm.7:00pm.8:00pm. Find the optimal solution. Yj= the number of part-time emplowees who start work beginning at howe i where i=1=11+00 a m, f=2= Noon, etel . Min s.t. 1160a.m. Noon 100p.m 2.000mm 3000m. 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 x1 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=11:00a.m,i=2= Noon, etc). Min s.t.11:00a.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,x6,x7,x8,y1,y2,y3,y4,y5,y6,y7,y8,y90 Find the optimal solution. 5:00p.m. 6:00p.m. 7:00p.m. 8:00p.m. 9:00p.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