Problem Set 5: Decision Analysis / Decision Trees You are the manager of a new hospital program designed to reduce the number of medical errors within a large health care system. Part of you duties is routinely checking the patient charts and ensuring the proper course of care was delivered, this includes dispensing the correct medications. proper services, and following treatment protocols. The hospital has realized that it can save money by limiting inappropriate treatments. The hospital wishes to explore the potential for expanding the number of chart pulls to either one in every 100 medical records, one in 50 charts, or one in 25 charts. Pulling more charts potentially means being able to identify more errors. You are unsure, however, if this would actually occur. You estimate that you may identify as many as 50 errors per year, 30 errors per year, or 10 errors per year. The average savings per error is estimated at $10,000. However, there is a cost associated with the additional pulls as well. To pull one in 50 records means hiring an additional staff person at $55,000 per year. Pulling one in 25 records means hiring a second staff person also at $55,000 per year. The probability that you will detect medical errors increases as you pull more charts, however the number or actual errors varies as does the efficiency to identify errors as you hire more people. You estimate that with one staff member you will detect 50 errors per year only 7% of the time, 30 errors per year 22% of the time and 10 errors per year 71% of the time. You further estimate that with two staff members you will detect 50 errors per year only 22% of the time, 30 errors per year 22% of the time and 10 errors per year 56% of the time. And you further estimate that with three staff members you will detect 50 errors per year only 31% of the time, 30 errors per year 33% of the time and 10 errors per year 36% of the time. You have based these probabilities running sample simulations by pulling small batches of charts. Given this information which option do you choose? Do you pull 1 in 100 charts with one staff person, I in 50 charts with 2 staff people or 1 in 25 charts with 3 staff people? Also, consider the mission of the organization. Does this affect your choice, and if so, demonstrate how you might make a financial case for this