Problem # $2$

Sheen came to believe after about six weeks of operation that demand for the Express could be

increased by adding a section that profiled people in the town and its suburbs, as well as state, national,

and international personalities. Her experiments suggested that demand was a function of the stylistic

quality and pictorial and information content of such a section; hence, of the amount of time she

invested in it$.$ Sheen had kept records of the time she had spent each day developing the profile section.

Using empirical data from the last few weeks, Sheen developed Figure $1$ to study the relationship on

any given day between the number of hours invested in creating the profile section and demand for

the Express.

$E(D)=500+\sqrt[\phantom{2}]{h}=500+50\sqrt[\phantom{2}]{h},$ where $D$ is daily demand for The Hamptonshire Express, and $h$

the number of hours Sheen has invested in creating the profile section.

As before, Sheen forecast demand for the following day's newspapers every evening based on the

quality of the profile section, and used her demand forecast to determine her stocking quantity.

a$.$ How many hours should Sheen invest daily in the creation of the profile section? Assume the

opportunity cost of her time $($based on other employment opportunities in Hamptonshire$)$ is

$$10$ per hour. Try different values for $h$ in the spreadsheet "Hamptonshire Express: Problem

#$2."($To make your life easier, the optimal stocking quantity, $Q,$ is computed by the spreadsheet

based on the newsvendor formula for your choice of $h.)$

b$.$ What explains Sheen's choice of effort level $h?$ Do not spend more than $10$ minutes thinking

about this question. $($Hint: The marginal cost of her effort is $$10$ per hour, the opportunity cost of her

time; the marginal benefit of her effort is $\frac{0\mathrm{.}8**50}{2\sqrt[\phantom{2}]{h}}.)$