# Stats

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Lemington’s is trying to determine how many Jean
Hudson dresses to order for the spring season.
Demand for the dresses is assumed to follow a normal
distribution with mean 400 and standard deviation
100. The contract between Jean Hudson and
Lemington’s works as follows. At the beginning of the
season, Lemington’s reserves x units of capacity.
Lemington’s 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 Hudson charges
\$50 per dress. If Lemington’s does not take delivery
on all x dresses, it owes Hudson a \$5 penalty for each
unit of reserved capacity that is unused. For example,
if Lemington’s orders 450 dresses and demand is for
400 dresses, Lemington’s will receive 400 dresses and
owe Jean 400(\$50)  50(\$5). How many units of
capacity should Lemington’s reserve to maximize its
expected profit?

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