MET AD 616 Assignment 1 - Revised - Michael Simons
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Boston University *
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AD 616
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Industrial Engineering
Date
Dec 6, 2023
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docx
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Assignment 1 – Michael Simons
Question 1 – Rnorm was used to determine the distribution for each site. These were then added together for as “Total”, and the mean and standard deviation of the total were determined. A histogram of the total was then created.
Question 2 – Parameters were added into R showing that the mean battery life is 7 years with a standard deviation of 2 years. Battery life was simulated using rnorm. A refund (if owed) is calculated as $10 + $1.50 * number of months owed. To determine if a refund is owed, the refund is only calculated if battery life was less than 5 years, otherwise the refund is $0. The average cost per phone is calculated using the mean of all simulation results, and the probability of owing a refund is calculated by determining the average number of times a refund was owed in the simulation out of the 100,000 results. The expected cost per refund is the average of all refunds that were greater than zero.
Question 3 – Each option was calculated using the below parameters, with each permutation changing the number of servings prepared. The daily demand was calculated using the rnorm function, with the revenue calculated using the
the lower of either the daily demand or the number of servings created multiplied by the price
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per cup. Costs are calculated as the number of servings multiplied by the cost per cup plus the license cost. Profit is shown as revenue minus costs, with the expected profit being the average profit generated across the 100,000 simulations. The code was run for each preparation, resulting in an average profit of:
75 = $54.21
100 = $96.94
120 = $120.13
140 = $131.54
160 = $131.66
180 = $124.30
Creating 160 servings results in the highest expected profit. A histogram was created for profit shows that, among all simulations, a majority of the days the stand sold all 160 servings and made the maximum profit possible on those days.