Make sure to include complete decision tree or influence diagrams.

(1) Westward Magazine Publishers are thinking of launching a new fashion magazine for women in the under -25 age group. Their original plans were to launch in April of next year, but information has been received that a rival publisher is planning a similar magazine. Westward now have to decide whether to bring their launch forward to January of next year, though this would cost an additional $500,000. If the launch is brought forward it is estimated that the chances of launching before the rival are about 80%. However, , if the launch is not brought forward it is thought that there is only a 30% chance of launching before the rival.

For simplicity , the management of Westward have assumed that the circulation of the magazine throughout its life will be either high or low. If Westward launch before the rival, it is thought that there is a 75% chance of a high circulation. However, if the rival launches first, the probability is estimated to be only 50%.

If the rival does launch first then Westward could try to boost sales by increasing their level of advertising. This would cost an extra $200,000, but it is thought that it would increase the probability of a high circulation to 70%. This increased advertising expenditure would not be considered if Westward's magazine was launched first. Westward's  accountants have estimated that a high circulation would generate  a gross profit over the magazine 'lifetime of $4 million. A low circulation would bring a gross profit of about $1 million . It is important to note; however; that these groups profit do not take into account additional expenditure caused by bringing the launch forward or by increased advertising.

(a) Draw a decision tree to represent Westward's problem.

(b) Assuming that Westward's objective is to maximize expected profit, determine the policy that they should choose. (For simplicity, you should ignore Westward's preference for money over time for example; for the fact they would prefer to receive a given case inflow now rather than in the future).

(c) In reality, Westward have little knowledge of the progress which has been made by the rival. This means that the probabilities given above for beating the rival (if the launch is , or note brought forward ) are very rough estimates. How sensitive is the policy you identified in (b) to change in these probabilities?

(2) Use an influence diagram to represent the following decision problem , stating any assumptions you have made.

(a) ABC Chemicals are planning to start manufacturing a new pharmaceutical product. Initially, they muse decide whether to go for a large-scale or small scale production. Having made this decision, the profits that they make will also depend on

(1) the state the economy over the next 2 years ;

(2) whether or not a rival manufacturer launches a similar product and

(3) the amount which ABC decides to spend on advertising the product (this decision will itself be influenced by the scale of production which ABC opt for, whether a rival product is launched and the state of the economy.

(b) Use your influence diagram to derive the outline of a decision tree which could be used to represent ABC's problem.