Exercise 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 has 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 rst. this probability is estimated to be only 50%. If the rival does launch rst 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 rst. Westward's accountants have estimated that a high circulation would generate a gross prot over the magazine's lifetime of $4 million. A low circulation would bring a gross prot of about $1 million. It is important to note, however, that these gross prots do not take into account additional expenditure caused by bringing the launch forward or by increased advertising. 1. Draw a decision tree to represent Westward's problem. 2. Assuming that Westward's objective is to maximize expected prot, determine the policy that they should choose. (For simplicity, you should ignore Westward's preference for money over time: for example. the fact that they would prefer to receive given cash inow now rather than in the future.) 3. 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 is not, brought forward) are very rough estimates. How sensitive is the policy you identied in (b) to changes in these probabilities