A store is trying to determine how many dresses to order for the next season. They believe that
demand for these types of dresses typically follows a gamma distribution with mean 400 and
standard deviation 100. The contract between the store and the supplier works as follows. At
the beginning of the season, the store reserves x units of capacity. The store must take delivery
for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for
$160 and the supplier charges $50 per dress. If the store does not take delivery on all x dresses,
it owes the supplier a $5 penalty for each unit of reserved capacity that is unused. For example,
if the store orders 450 dresses and demand is for 400 dresses, the store will receive 400 dresses
and owe the supplier 400($50) + 50($5).
a) Develop a simulation model to address the following question: What should be the optimal
capacity to reserve that would maximize the store’s expected profit? (please make sure to
attach your R code for your simulation model). Use a simulation size of 10,000.
b) For the optimal capacity from part a, compute the probability that profit will be negative.
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