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 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 xi= the number of part-time employees who start work beginning at hour i where i=1=11:00 a.m., i=2= Noon, etc) . Min30.4x1+30.4x2+30.4x3+30.4x4+30.4x5+30.4x6+30.4x7+30.4x8 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. 9:00p.m.x86x1,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 Seven surplus employees are scheduled for 2pm3pm, and four for 8pm9pm, suggesting that employees should be rotated off earlier (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 i where i=1=11:00 a.m., i=2= Noon, etc). Mins.t.11:00a.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. Find the optimal solution. (x1,x2x3x4x5x6x7x8y1y2y3y4y5y6y7,y8y9)=(x8=6,y1=8,y3=1,y5=1,y7=4