Write the complete linear programming model and develop
Anderson 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.Time Total Number of Employees Needed11:00 a.m.�Noon 9Noon�1:00 p.m. 91:00 p.m.�2:00 p.m. 92:00 p.m.�3:00 p.m. 33:00 p.m.�4:00 p.m. 34:00 p.m.�5:00 p.m. 35:00 p.m.�6:00 p.m. 66:00 p.m.�7:00 p.m. 127:00 p.m.�8:00 p.m. 128:00 p.m.�9:00 p.m. 79:00 p.m.�10:00 p.m. 7One full-time employee comes on duty at 11:00 A.M., works 3 hours, takes an hour off, and returns for another 5 hours. The other full-time employee comes to work at 1:00 P.M. and works the same 3-hours-on, 1-hour-off, 5-hours-on patternA. Write the complete linear programming model and develop a minimum-cost schedule for part-time employees.B. What is the total payroll for the part-time employees? How many part-time shifts are needed? 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. Write the complete linear programming model and develop a minimum-cost schedule for the part-time employees. How many part-time shifts are needed, and what is the cost savings compared to the previous schedule?D. The restaurant decides to give part-time employees a raise to $8.50 per hour. how much this program will increase the cost?Use the results of ranges of optimality and feasibility for the model in part c to answer the following questions:E. Explain the meaning of dual values for constraints 1, 2, and 3. (-15.2, -7.6, and 0)F. How come there are no 4-hr part timers scheduled until 6PM? What does it take for 4-hr part timers to be sheduled at 1PM and 4PM?
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