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 full-time and part-time employees needed varies with the time of day as shown. Time Number of Employees Needed 11:00 a.m.–Noon 9 Noon–1:00 p.m. 9 1:00 p.m.–2:00 p.m. 9 2:00 p.m.–3:00 p.m. 3 3:00 p.m.–4:00 p.m. 3 4:00 p.m.–5:00 p.m. 3 5:00 p.m.–6:00 p.m. 6 6:00 p.m.–7:00 p.m. 12 7:00 p.m.–8:00 p.m. 12 8:00 p.m.–9:00 p.m. 7 9:00 p.m.–10:00 p.m. 7 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). 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, x6, x7, x8 ≥ 0 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. This answer has not been graded yet. (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). 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, x6, x7, x8, y1, y2, y3, y4, y5, y6, y7, y8, y9 ≥ 0 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 $) compared to the previous schedule? part-time shifts neededcost savings$

The Fore and Aft Marina is located on the Ohio River near Madison, Indiana. Fore and Aft currently operates a docking facility where only one boat at a time can stop for gas and servicing. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume that the arrival rate is 3 boats per hour and that the service rate for each server is 9 boats per hour. (Round your answers to four decimal places.) (a) What is the probability that the boat dock will be idle? (b) What is the average number of boats that will be waiting for service? (c) What is the average time (in hours) a boat will spend waiting for service? h (d) What is the average time (in hours) a boat will spend at the dock? h (e) If customers expect to be able to be in and out of the marina within 10 minutes on average, does this system provide acceptable service? ---Select--- V since the average time a boat will…

Students at Upscale University are required to take at least 3 humanities and 4 science courses. The maximum allowable number of science courses is 12. Each humanities course carries 4 credits and each science course 5 credits. The total number of credits in science and humanities cannot exceed 88. Quality points for each course are assigned in the usual way: the number of credit hours times 4 for an A grade, times 3 for a B grade, and times 2 for a C grade. Susan Katz expects to get B's in all her science courses. She expects to get C's in half of her humanities courses, B's in one-fourth of them, and A's in the rest. Under these assumptions, how many courses of each kind should she take in order to earn the maximum possible number of quality points? Susan Katz should take science courses and humanities courses in order to maximize her quality points.

A retailer anticipates selling 1,300 units of its product at a uniform rate over the next year. Each time the retailer places an order for a units, it is charged a flat fee of $25. Carrying costs are $26 per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost? They should order units The minimum inventory cost is $ times a year.