# At the optimal level, what is the expected (average) weekly profit?

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November 30, 2020
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A pharmacy carries a perishable product that must be sold within a week of being purchased. The pharmacy purchases the
A pharmacy carries a perishable product that must be sold within a week of being purchased. The pharmacy purchases the product for \$50 per unit, and sells it to its customers for \$75 per unit. If the pharmacy does not have enough units on stock to satisfy the demand, a rush order must be placed, at a cost of \$100 per unit; however, the pharmacy must still sell the product for \$75 per unit. Any unsold units of the product must be discarded at the end of the week. Based on past experience, the pharmacy knows that in any given week the demand for this product can be approximated by a normally distributed random variable with a mean of 11 units and a standard deviation of 2 units.Assuming that the pharmacy wants to maximize average weekly profits, use Monte Carlo simulation (Palisade Decision Tools @Risk) to determine the optimal number of units of the product to stock every week. -a) At the optimal level, what is the expected (average) weekly profit? -b) Produce a histogram showing the distribution of weekly profits if the pharmacy stocks 7 units of the product every week. -c) Produce a histogram showing the distribution of weekly profits at the optimal level. -d) Produce a 95% confidence interval for the weekly profits at the optimal level.

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