My comment: "By analyzing the surplus variables in the linear programming solution, we can identify that certain constraints are underutilized.

For instance, the constraint for employees starting at noon has 8 surplus employees (with x1 = 8 and x2 = 0).

This indicates the potential to schedule some employees for shorter shifts, such as 3 hours, during this time period.

This would optimize their time usage, increase efficiency, and lead to cost savings."

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 4hour 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. ne 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 ull-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). Min(x1+x2+x3+x4+x5+x6+x7+x8)7.64 s.t. 11:00 a.m. Noon x1+x2+19 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. x3+x4+x5+x6+23 5:00 p.m. 6:00 p.m. x5+x6+x7+x8+2>=12 7:00 p.m. x6+x7+x8+2>=12 8:00 p.m. x7+x8+1>=7 9:00 p.m. x8+1>=7 x1,x2,x3,x4,x5,x6,x7,x80 Find the optimal solution. (x1,x2,x3,x4,x5,x6,x7,x8)=(8,0,0,1,2,1,5,10) (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. By analyzing the surplus variables in the linear programming solution, we can identify that certain constraints are underutilized. For instance, the constraint for employees starting at noon has 8 surplus employees (with x1=8 and x2=0 ). Score: 0.64 out of 0.64 Comment: 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). Min s.t. 11:00am. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. x2+x3+x4++x5+y52 4:00 p.m. 5:00 p.m. 6:00 p.m. x5+x6+x7+x8+y810 7:00 p.m. 8:00 p.m. Check which variable(s) should be in your answer. 9:00 p.m