# Thread: Stat S2 level Question

1. ## Stat S2 level Question

An indoor tennis centre has five courts which are booked by members of the public, usually over the telephone.
Demand for each hour in the peak-period hours, i.e. 4pm to 11pm, has been found to rise to a Poisson distribution with a mean of 9 if the tennis centre continues to charge its off-peak rate of £6 per court per hour. The centre management is therefore considering setting the price at a higher level during the peak period. In fact they have experimented with different prices and have found the following demand levels:

Price (per ct per hr) | Mean Hourly Demand
£6 _____________|______9
£7 _____________|______8
£8 _____________|______7
£9 _____________|______6
£10 _____________|______5
£11 _____________|______4
£12 _____________|______3

(i) What proportion of demand would be turned away if the peak-period price is set at the current off-peak price of £6 per court per hour, and what hourly income would be generated?
(ii) At what level should they set the peak-period price in order to maximise the average hourly income during the peak period?
(c) Explain briefly what further information you would require and what analysis you would undertake to investigate whether or not it would be profitable for the tennis centre to open a sixth court. There is no need to do any calculations.