The newly-established pediatric department of a local hospital is in need of full-time nurses who will work in 8-hour shift per day and part-time nurses who will work in 4-hour shifts per day. Each day is divided into 6 four-hours periods, which requires different number of nurses., as shown in the table below: Time Period Index Time Period Covered 7am - 11am 11am-3pm 3pm - 7pm 7pm-11pm 11pm-3am 3am - 7am 1 2 3 4 5 6 Required Number of Nurses 7 9 12 5 4 3 The shifts of full-time nurses can begin at the start of any of the four-hour periods. Hospital policy requires that there must be at least two full-time nurses at each time period. Also, the number of part-time nurses cannot exceed the number of full-time nurses in any time period. Full-time nurses get paid at $160 per shift, while the part-time nurses get paid at $50 per shift. Formulate a linear programming model that will determine the nursing schedule so as to minimize the total cost.
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- Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) L (average units in units system) La (average units waiting in queue) units W (average time in the weeks system) Wq (average time in the queue) weeks c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the…Chapter 5. (M/M/s/K Model). Leia is responsible for 12 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 4 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $750 per week per computer and $800 per week of…Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would bel units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) Performance Measures c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines? PO (probability that sytem is empty) % dollars L (average units in system) units d. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per…
- Note: Excel please! The workload in many areas of bank operations has the characteristics of a nonuniform distribution with respect to time of day. For example, at Chase Manhattan Bank, the number of domestic money transfer requests received from customers, if plotted against time of day, would appear to have the shape of an inverted-U curve with the peak reached around 1 P.M. For efficient use of the resources, the manpower available should, therefore, also vary correspondingly. A variable capacity can effectively be achieved by employing part-time personnel. Since part-timers are not entitled to all fringe benefits, they are often more economical than full-time employees. However, other considerations may limit the extent to which part-time people can be hired in a given operating department. The problem is to find an optimum workforce schedule that would meet manpower requirements at any given time and also be economical. Some of the factors affecting personnel assignments can be…A machine tool company conducts a job-training programme at a ratio of one for everyten trainees. The training programme lasts for one month. From past experience it has been found thatout of 10 trainees hired, only seven complete the programme successfully. (The unsuccessful traineesare released). Trained machinists are also needed for machining. The company's requirement for thenext three months is as follows:January: 100 machinists, February: 150 machinists and March: 200 machinists.In addition, the company requires 250 trained machinists by April. There are 130 trained machinistsavailable at the beginning of the year. Pay roll cost per month is:Each trainee Rs. 400/- per month.Each trained machinist (machining or teaching): Rs. 700/- p.m.Each trained machinist who is idle: Rs.500/- p.m.(Labour union forbids ousting trained machinists). Build a l.p.p. for produce the minimum costhiring and training schedule and meet the company’s requirement.Chapter 5. (M/M/s/K Model). Leia is responsible for 12 dataunits in the IT offices in a small business called DataWish. Each dataunit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each dataunit for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/S/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the weeks system) Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per dataunit and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the…
- A machine used for cutting materials in a factory has the following outputs per hour at various speeds and required periodic tool regrinding at intervals cited. Speed Hour Output per Tool RegrindingA 200 pieces every 8 hours B 280 pieces every 5 hours A set of tools costs 560 and can be ground twenty times. Each regrinding costs 54.00 and the time needed to regrind and change tools is 1 hour. The machine operator is paid 35.00 per hour including the time the tool is changed. The tool grinder who also sets the tools to the machine is paid 40.00 per hour. The hourly rate chargeable against the machine is 38.00, regardless of machine speed. Which speed is more ecomical? A. Speed B, 0.096/pc B Speed B, 0.087/pc C. Speed A, .054/pc D. Speed A >037/pcA company makes two products (A and B). Each product requires time on two machines 1 and 2. the specifications for each product are as follows Product A Product B Processing time on machine 1 (hrs/unit) Processing time on machine 2 (hrs/unit) Material and labor cost (Sh./ unit) Selling price (Sh./ unit) Maximum possible sale (units) 2 1 2 14 15 16 18 130 150 The amount of time available on machine 1 is 360 hrs and on machine 2 is 260 hrs. Using simplex method determine the number of product A and B, which should be sold in order to maximize total contribution for the company.Rollmore, a non-union manufacturing company decides it needs input on improving its work processes and procedures and decides to create employee committees to provide general feedback about things such as work rules and organizational policies and practices in hopes of improving efficiency. Rollmore asks ten employees to serve on such committees. Rollmore asks these employees to bring to their meetings, which include management representatives, concerns and ideas from their coworkers. Rollmore schedules these committees to meet once a month for two hours and provides lunch and a conference room for the participants. Are these employee committees legal or illegal? Why or why not?
- Chapter 5. (M/M/s/K Model). Leia is responsible for 13 data units in the IT offices in a small business called DataWish. Each data unit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each data unit for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per data unit and $800 per…JOHNSON’S RULE Five specialty jobs at a La Crosse, Wisconsin, tool and die shop must be processed through two workcenters (drill press and lathe). The time for processing each job follows:Work (processing) Time for Jobs (hours)JOBWORK CENTER 1(DRILL PRESS) WORK CENTER 2(LATHE)A5 2B3 6C8 4D 10 7E 7 121) An operator is used for loading and unloading of parts to automated machines. Loading time is 1 minute; unloading time is 2 minutes, machining time is 30 minutes, Operator travel time between the machines including the inspection time is 4 minutes. Cost of operator is C₁=40 TL/Hour, cost of a machine is C₂-200 TL/Hour. What is the cost per unit of production if optimum number of machines is assigned to the operator? (Note: Times are given in minutes and costs are per hour) a) 231 TL/unit b) 6930 TL/unit c) 115.5 TL/unit d) 240 TL/unit e) 132 TL/unit 2) An operator is used for loading and unloading of parts to automated machines. Loading time is 1 minute; unloading time is 2 minutes, machining time is 30 minutes; Operator travel time between the machines including the inspection time is 4 minutes. Cost of operator is C1=40 TL/Hour; cost of a machine is C₂=200 TL/Hour. How many machines (integer number) should be assigned to the operator so that the total operator and machine costs…