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 $600$ and standard deviation $150.$ 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 $0\mathrm{.}8$x 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? Try units of capacity from $400$ to $900,$ with increments of $50$ units. Round your answer to the nearest whole number, if necessary.

Optimal units of capacity: