Essentials Of Investments686 solutions
A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.
A manufacturing company has been inspecting units of output from a process. Each product inspected is evaluated on five criteria. If the unit does not meet standards for the criteria it counts as a defect of the unit. Each unit could have as few as zero defects, and as many as five. After inspecting 2,000 units, they discovered 33 defects. What is the DPMO measure for this process?
Question:An enterprising student has set up an internship clearinghouse for business students. Each student who uses the service fills out a form and lists up to 10 companies that he or she would like to have contacted. The clearinghouse has a choice of two methods to use for processing the forms. The traditional method requires about 20 minutes to review the form and arrange the information in the proper order for processing. Once this setup is done, it takes only two minutes per company requested to complete the processing. The other alternative uses an optical scan/retrieve system, which takes only a minute to prepare but requires five minutes per company for completing the processing. If it costs about the same amount per minute for processing with either of the two methods, when should each be used?
The state and local police departments are trying to analyze crime rates so they can shift their patrols from decreasing-rate areas to areas where rates are increasing. The city and county have been geographically segmented into areas containing 5,000 residences. The police recognize that not all crimes and offenses are reported: People do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 1,000 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area
An engineering firm retains a technical specialist to assist four design engineers working on a project. The help that the specialist gives engineers ranges widely in time consumption. The specialist has some answers available in memory, others require computation, and still, others require significant search time. On average, each request for assistance takes the specialist one hour. The engineers require help from the specialist on average of once each day. Because each assistance takes about an hour, each engineer can work for seven hours, on average, without assistance. One further point: Engineers needing help do not interrupt if the specialist is already involved with another problem. Treat this as the finite queuing problem and answer the following questions:
Question: The state and local police departments are trying to analyze crime rates so they can shift their patrols from decreasing-rate areas to areas where rates are increasing. The city and county have been geographically segmented into areas containing 5,000 residences. The police recognize that not all crimes and offenses are reported: People do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of 1,000 of the 5,000 residences for data on crime. (Respondents are guaranteed anonymity.) Here are the data collected for the past 12 months for one area:
Question: The flow of materials through eight departments is shown on the next page. Even though the table shows flows into and out of the different departments, assume that the direction of flow is not important. In addition, assume that the cost of moving material depends only on the distance moved.
Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high-crime areas should have more police protection than low-crime areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or cleaning up abandoned areas and buildings) should be used proportionately to crime occurrence. In a fashion similar to problem 11, the city has been broken down into 20 geographic areas, each containing 5,000 residences. The 1,000 samples from each area showed the following incidence of crime during the past month
L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two nurses. The special injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day, patient load drops, and only one nurse is needed to administer the injections. Let’s focus on the simpler case of the two—namely when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an inter-arrival time of approximately three minutes. It takes the nurse an average of two minutes to prepare the patients’ serum and administer the injection.
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