Please note the numbers may change from one question to another.

A publisher sells books to Barnes $\backslash$& Noble at $\backslash$$$14$ each. The unit cost for the publisher is $\backslash (\backslash$$ $2\backslash )$ per book. Barnes $\backslash$& Noble prices the book to its customers at $\backslash (\backslash$$ $40\backslash )$ and expects demand over the next two months to be normally distributed, with a mean of $30,000$ and a standard deviation of $8,000.$ Barnes $\backslash$& Noble places a single order with the publisher for delivery at the beginning of the twomonth period. Currently, Barnes $\backslash$& Noble discounts any unsold books at the end of two months down to $\backslash (\backslash$$ $2\backslash ),$ and any books that did not sell at full price sell at this price.

A plan under discussion is for the publisher to refund Barnes $\backslash$& Noble $\backslash$$$2$ per book that does not sell during the two$-$month period. Because Barnes $\backslash$& Noble shares the point$-$of$-$sales data with the publisher, the publisher does not require Barnes $\backslash$& Noble to return all unsold books for verification purpose. Thus, Barnes $\backslash$& Noble can still sell any unsold books at $\backslash$$$2$ each at the end of two month period.

With the arrangement of the refund paid by the publisher for any unsold books, what is the unit overage cost for Barnes $\backslash$& Noble?