In a number of advance purchase contracts, it is possible to get a lower rate by committing to a purchase quantity. This happens, for instance, when you make a booking for catering of an event such as a corporate retreat. In the example considered here, a local resort where you want to organize an event requires that you specify in advance how many people will be there (call this the order amount). It charges a discounted per person price of $150 for this amount. There are no refunds if fewer people show up. However, the resort will accommodate last-minute requests for additional attendees at a cost of $250 per person. As the organizer, you are trying to minimize the cost of the event.

In the past, there has been considerable variation in the number of people who show up. After some thought, you decide that no fewer than 125 people will show up, that the most likely number showing up will be 175, and the maximum number showing up can be 275. Hence you decide to model the number of people showing up using a triangular distribution with these three parameters. This distribution can generate a non-integer number of people showing up – so round to the nearest integer.

1. What is the @Risk formula that describes (generates) the random number of people showing up for the picnic?
2. [2 points] Suppose you decide to estimate the number of people showing up at the picnic by the number most likely to show up (i.e. 175). This is entered as the order amount. Construct the @Risk model that will allow you to compute the cost of the picnic to the company. Use the model to compute (i) the expected cost, (ii) the standard deviation, and (iii) maximum cost. Include your annotated @Risk model as Exhibit D (using FORMULATEXT to display formulae). [Run the simulation for 500 iterations using a random number generator seed of 123.]

3. Now use the simulation model to come up with the optimal order amount to specify in the contract from the following possibilities: 160, 165, 170, 175, 180, 185, 190, and 195.

4. Suppose the charge for additional attendees is $350 instead of $250. Does this change your optimal order amount? How? What if the charge for additional attendees is the same (i.e. $150)?