# A new book is to be launched by a publishing firm to catch the Christmas market.

A new book is to be launched by a publishing firm to catch the Christmas market. The manager of the

firm wants to know how many books to print for this time-limited market. If she prints too few, she

will miss the opportunity for profit. If she prints too many, she will have a lot of books left over in the

New Year which will have to be sold off at a loss. Suppose every book sold before Christmas makes a

profit of £15 whilst the publishing firm loses £5 for every book left over after Christmas. The

pre-Christmas demand for the book has a probability distribution given in the table below.

Calculate (in units of 1000 books) the expected demand for the book, and the standard deviation in

this demand.

Calculate figures for a third column to the table, equalling the profit (in units of £1,000) for each

amount sold if the print run is 23,000 books. What is the return (expected profit) in this case?

Calculate the print run size that will maximise the expected profit. What is the risk associated with

this strategy? Support your answers by calculating expected profit figures for each possible stock

level in a table.

firm on her strategy.

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