A ticket agent has an arrangement with a concert hall that holds concerts on 60 nights a
Question:
A ticket agent has an arrangement with a concert hall that holds concerts on 60 nights a year whereby he receives discounts as follows per concert:
Purchases must be in full hundreds. The average price per ticket is £3.
The information available is as follows:
He must decide in advance each year the number of tickets he will purchase.
He must return any tickets unsold by the afternoon of the concert to the ticket office. If the ticket office sells any of these he receives 60% of their price.
His sales records over a few years show that for a concert with extremely popular artists, he can be confident of selling 500 tickets, for one with lesser known artists 350 tickets, and one with relatively unknown artists 200 tickets.
His records also show that 10% of tickets he returns are sold in the ticket office.
s His administration costs incurred in selling tickets are the same per concert irrespective of the popularity of the artists.
There are two possible scenarios in which his sales record can be viewed:
Scenario 1: that, on average, he can expect concerts with lesser known artists.
Scenario 2: that the percentage frequency of concerts will be:
Required
(a) Separately for each of scenarios 1 and 2 calculate:
(i) the expected demand for tickets per concert; and (ii) first, the level of the agent’s purchases of tickets per concert that will give him the largest profit over a long period of time; and secondly, the profit per concert that this level of purchases of tickets will yield.
(b) For scenario 2 only, calculate the maximum sum per year that the ticket agent should pay to a concert specialist for 100% correct predictions as to the likely success of each concert.
Step by Step Answer:
