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Math and statistics for business

Paper, Order, or Assignment Requirements

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.

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

standard deviation of this demand. [25 marks]

(ii) 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? [Note that (a) even if the demand is greater than

23,000, only 23,000 books will be sold; (b) when the demand is less than 23,000,

unsold books will have a negative impact on profits.] [25 marks]

(iii) By repeating (ii) for different print run sizes, calculate the print run size that will

maximise the expected profit. What is the risk (standard deviation) associated with

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

possible stock level in a table.