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) ____£6__£7__£8__£9__£10__£ 11__£12
Mean Hourly Demand_____9___8___7___6____5___ _4____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?
I actualy did it, but my friend, has different answer, and I'm not sure who's method is corect. Please tell how you would do it?
And actually passed?