Posted by **Kod** on Monday, March 4, 2013 at 1:19pm.

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?