Solve the following questions using Excel QM. (24 = 8 marks)
- Q(1) Helping others through blood donation is a form of social solidarity or social responsibility. The blood donors cite a sense of social responsibility as their reason for donating blood, and as a result, the communities value and reward this activity. The following table shows the number of blood donors in a university from 20112023. Develop a 3-year moving average forecast and obtain the related statistical measures using excel QM.
- Q(2) University X has a unique on-campus dispensary that provides medical care. On a typical working day, patients arrive at the dispensary at an average rate of 2 patients per hour. There is one single nurse at the dispensary, and the average time required to give a consultation is 12 minutes.
It is assumed that the service times can be described by the exponential distribution, and the arrival process by a Poisson distribution. You are requested to find:
- The average time in line,
- The average number of patients in line,
- The average time in the system,
- The average number of patients in the system,
- The probability that the dispensary is empty,
- The utilization factor of the system.
- Q(3) Assume that you are a statistical consultant and want to provide a volunteer consultation to a start-up company as a social responsibility consultation. The company is planning to purchase a uniform outfit for their employees, and they obtained the following quantity discount table with three discount options:
- Annual demand is 400 outfits, ordering cost is50, and holding cost is 25% of the cost of the outfit. Use Excel QM to find thediscount option with the minimum total cost.
- Q(4) To help needy peoplethrough charity is a form of social responsibility. The act of doing charity tohelp others is recognized and rewarded by all communities of the society. Thefollowing table shows the amount collected through charity and the amount spenton social development (in million dollars) in the last 8 years. Find thecorrelation and coefficient of determination for the given data and obtain therelated statistical measures using excel QM.
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