An engineer is driving her car to attend an important meeting in a nearby town. The meeting is scheduled to begin in another 90 minutes. She judges that if she stays within the speed limit, her travel time will be uniformly distributed over 2 ‡ 0.6 hours. However, if she decides to exceed the speed limit, by an mph, her travel time will decrease and be uniformly distributed over (2- I/20) ‡ 0.6 hours. In this case, however, she runs the risk of getting a speeding ticket; this probability being given by a/25 for 0 < 2 < 25. Suppose that the loss associated with the delay in attending the meeting is equal to the amount of the delay (in hours). If the engineer is ticketed, 0.3 hours needs to be added to her travel time; in addition, the loss resulting from the traffic ticket is r/ 30 (which also depends on how much faster than the speed limit she is going). Assume that there is no other loss. Formulate the decision problem and determine her optimal excess speed.

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