Concept explainers
a)
To determine: The number of police officers needed.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
b)
To use: The solver table to determine the way the number of police officers changes as the number of police required from midnight to 4 A.M. changes.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
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Practical Management Science
- The Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A patrol car requiresrepairs every 30 days, on average, according to an exponential distribution. When a patrol car is in need of repair it isdriven into the motor pool, which has a repairperson onduty at all times. The average time required to repair a patrol car is 12 hours (exponentially distributed). Determinethe average time a patrol car is not available for use and theaverage number of patrol cars out of service at any onetime, and indicate if the repair service seems adequatearrow_forwardJoan has a small design and tailoring shop making custom outfits for women. She has two employees. Each employee only begins working on a dress when a customer order has been received and then she makes the dress from beginning to end. The average production time of a dress is 1.8 days, with a standard deviation of 2.1 days. Historically, Joan has been receiving orders with interarrival times of one day on average. The interarrival times of orders have a coefficient of variation of one. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected waiting time, in days, between when an order is received and when production begins on the dress? A. 9.12 days B. 6.50 days C. 1.23 days D.3.41 daysarrow_forwardYour company has a very complex conveyor system in the warehouse. The conveyors take product from a receiving dock and route them to one of ten different shipping points on the shipping dock. The conveyors are controlled by computers. You need to find an employee maintain this computer system on the night shift. Your assignment recruit an employee to fill this position. How would find a qualified candidate?arrow_forward
- Catherine Blake, the office manager for the College of Business Administration, has received numerous complaints lately from several department chairpersons. In the past few months, the chairpersons have insisted that something be done about the amount of time their administrative assistants waste waiting in line to make copies. Currently, the college has two photocopy centers dedicated to small copying jobs: copy center A on the third floor and copy center B on the fourth floor. Both centers are self-serve and have identical processing capabilities. The copying machines are not visible to the administrative assistants from their offices. When copying is required, the administrative assistant goes to the copy room and waits in line to make the necessary copies. Catherine’s assistant, Brian, was assigned to investigate the problem.Brian reported that, on average, administrative assistants arrive at copy center A at the rate of 10 per hour and at copy center B at the rate of 14 per…arrow_forwardOffice Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer's business site within an average of three hours from when the customer notifies OEI of an equipment problem. Currently, OEI has ten customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. Suppose the service technician is available when a customer calls for service. In that case, it takes the technician an average of 1 hour of travel time to reach the customer's office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer…arrow_forwardOffice Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem. Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer’s office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new…arrow_forward
- An insurance company receives 220 calls per day from customers who lodge insurance claims. The call center is open from 8 a.m. to 5 p.m. The arrival of calls follows a Poisson process. Looking at the intensity of arrival of calls, we can distinguish three periods during the day: the period 8 a.m. to 11 a.m., the period 11 a.m. to 2 p.m. and the period 2 p.m. to 5 p.m. During the first period, around 60 calls are received. During the 11 a.m. to 2 p.m. period, 120 calls are received, and during the 2 p.m. to 5 p.m. period, 40 calls are received. A customer survey has shown that customers tend to call between 11 a.m. and 2 p.m. because during this time they have a break at work. Statistical analysis shows that the durations of calls follow an exponential distribution. According to the company’s customer service charter, customers should not wait more than 1 min on average for their call to be answered. • Assume that the call center can handle 70 calls per hour using 7 call center…arrow_forwardAt Trojans Urgent Care Clinic, there is one triage nurse, 5 nurse practitioners, and 3 doctors. Patients arrive to the triage nurse, and the triage nurse decides if their case can be handled by a nurse practitioner or must be handled by a doctor. The triage nurse can detect patients whose case can be handled by a nurse practitioner in on average 5 minutes with standard deviation 1 minute; however, the triage nurse spends on average 10 minutes with standard deviation 3 minutes with patients whose case is eventually handled by a doctor. Patients seeing a nurse practitioner spend on average 30 minutes with standard deviation 8 minutes with the nurse practitioner, and patients seeing a doctor spend on average 45 minutes with standard deviation 10 minutes with the doctor. 60% of arriving patients are cared for by a nurse practitioner and 40% of arriving patients are cared for by a doctor. Patients leave the Urgent Care Clinic after seeing either the nurse practitioner or the doctor. a) If 8…arrow_forwardThe College of Business and Public Administration at Benton University has a copy machine on each floor for faculty use. Heavy use of the five copy machines causes frequent failures. Maintenance records show that a machine fails every 2.5 days (or π = 0.40 failure/day). The college has a maintenance contract with the authorized dealer of the copy machines. Because the copy machines fail so frequently, the dealer has assigned one person to the college to repair them. The person can repair an average of 2.5 machines per day. Using the finite-source model, answer the following questions:a. What is the average utilization of the maintenance person?b. On average, how many copy machines are being repaired or waiting to be repaired?c. What is the average time spent by a copy machine in the repair system (waiting and being repaired)?arrow_forward
- In queueing theory, how is the exponential distribution the most relevant probability distribution?arrow_forwardScenario Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem. Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer’s office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a…arrow_forwardFatema, Mariam, and Layan are three dental hygienists who work for Dr. Amnah at Family Dentistry. All three hygienists do pretty much the same thing every day. On an average, they see 12 people every day for regular teeth cleaning which involves cleaning, flossing, and normal checkup. Dr. Amnah, on the other hand, has quite unpredictable job. She has to respond to all types of teeth-related emergencies including having to do surgeries. All three hygienists always try to help each other out, have a very good attitude in general toward each other, and keep each other informed about matters that are relevant to them and to Dr. Amnah. Fatema specifically takes on the role of attending all community-related voluntary meetings and functions where Family Dentistry may have a stake or are asked for involvement. On her own time, she keeps up on all dental regulations and business-related news that may have an impact on the firm. Mariam speaks up and offers constructive suggestions regarding…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,