A manager at a sporting goods store has to decide on a number of shoes to purchase

for a sporting event. Bases on past demand data, the manager has forecast demand to

be normally distributed, with a mean of $300$ and a standard deviation of $90.$ The store

gets $$180$ for each pair of shoes sold at the event, but loses $$20$ on every pair of shoes

unsold at the end of the event. How many pairs of shoes should the manager reorder?