2. A department store needs to hire holiday season sales staff for their store. To cover all the responsibilities, they know that they need to have at least 20 workers on Sundays, 15 on Mondays, 16 on Tuesdays, 16 on Wednesdays, 16 on Thursdays, 22 on Fridays, and 22 on Saturdays. Staff members are guaranteed two consecutive days off. At a minimum, how many staff members need to be hired in order to ensure that the store can remain fully staffed every day of the week? a. Formulate an Integer LP (ILP) for this problem in Excel. b. Solve your model for the optimal solution.
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- b. The Healthy Food Restaurant, a 24-hour restaurant, faces changing requirements from hour tohour. More workers are needed for peak hours, and fewer are needed in between. The followingTable 6 (below) shows the worker requirement for the first 12 hours in the restaurant:Table 6. Staff Requirement at the Healthy Food RestaurantTime Period 10AM11AM12PM1PM2PM3PM4PM5PM6PM7PM8PM9PMRequirement 8 10 12 12 9 7 6 7 9 10 12 8AssignedOn DutyOverstaffed8(i) You are required to apply the first-hour principle to staff each hour with the required number ofcafeteria staff, showing how many staff are on duty each given hour, the number of staffyou have assigned to work each hour and any overstaffing for each hour. i. Schedule the staff to work in 8-hour shifts.4. The Spencer Optics Company produces an inexpensive line of sunglasses. The manufacturing process consists of assembling two plastic lenses (produced by the firm's plastic molding depart- ment) into a finished frame (purchased from an outside supplier). The company is interested in using material requirements planning to schedule its operations and has asked you to prepare an example to illustrate the technique. The firm's sales manager has prepared a 10-week sales forecast for one of the more popular sunglasses (the Classic model) for your example. The forecast is 100 units per week. Spencer has customer orders of 110 units, 80 units, 50 units, and 20 units in weeks 1, 2, 3, and 4, respectively. The sunglasses are assembled in batches of 300 units. Presently, three such batches are sched- uled: one in week 2, one in week 5, and one in week 8. Complete the following time-phased record: Week hand 1 2 3 4 5 6 7 8 9 10 Classic Model On MPS Record Forecast Orders Projected available…4. The seven-person maintenance function at a hospital performs both preventive and corrective maintenance on hundreds of items each month, All the workers are scheduled for 40 hours per week and there are four weeks in a month. It is the goal of the maintenance department to achieve 90% utilization with a mix of two-thirds preventive maintenance and one-third corrective maintenance, How many hours each month are spent performing preventive maintenance if they achieve their 90% utilization and correct/preventive mix targets?
- 4. The seven-person maintenance function at a hospital performs both preventive and corrective maintenance on hundreds of items each month. All the workers are scheduled for 40 hours per week and there are four weeks in a month. It is the goal of the maintenance department to achieve 90% utilization with a mix of two-thirds preventive maintenance and one-third corrective maintenance. How many hours each monthOre spent performing preventive maintenance if they achieve their 90% utilization and correct/preventive mix targets? 6. Focus ר DELLWilliam Beebe owns a small shoe store. He has 10 pairs of shoes that requireresoling and polishing. He has a machine that can resole one pair of shoes at atime, and the time required for the operation varies with the type and condition of theshoe and the type of sole that is used. Shoes are polished on a machine dedi-cated tothis purpose as well, and polishing is always done after resoling. His assistant generally does the polishing while Mr. Beebe does the resoling. The resoling and polishingtimes (in minutes) are Shoes Resoling Time Polishing Time1 14 32 28 13 12 24 6 55 10 106 14 67 4 128 25 89 15 510 10 5In what order should the shoes be repaired in order to minimize the total makespanfor these 10 jobs?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 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…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…Because of its labor contract, a company must hire enough labor for 100 units ofproduction per week on one shift or 200 units per week on two shifts. It cannot hire,lay off, or assign overtime. During the fourth week, workers will be available fromanother department to work part or all of an extra shift (up to 100 units). There is aplanned shutdown for maintenance in the second week, which will cut production tohalf. Develop a production plan. The opening inventory is 200 units, and the desiredending inventory is 300 units
- 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…A diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and atleast 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units of Vit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit.A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and eachbrand Y capsule costs P9.00, how many capsules should the patient take each day tominimize the costs? Solve using graphical method. Show complete solution.Consider a law firm with 15 lawyers and 3 paralegals. The firm is struggling to keep up with the high demand for its services, particularly during the busy litigation seasons. It has been observed that the lawyers spend a significant amount of their time on administrative tasks that could potentially be handled by paralegals. After a careful study of the work distribution within the firm, it was determined that 35% of the activities carried out by the lawyers are administrative in nature. Given that each lawyer works 50 hours a week, please determine: (a) How many additional paralegals should the firm hire to handle the administrative tasks currently performed by the lawyers? (b) If the lawyers' time spent on administrative tasks is redirected to billable legal work, by what percentage could the firm potentially increase its billable hours?