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The year is 2022 and today is July 1 (by assumption). You plan to fly from Newark to Amsterdam on August 2 and return on August 25. Today you can buy a one-way ticket for $350 or a round-trip ticket for $660. You could also wait until August 1 to buy your tickets. On August 1, a one-way ticket in either direction will cost $370, and a round-trip ticket will cost $730. Between July 1 and August 1, there is a 30% chance that your best friend will be able to provide you with a free one-way ticket as a present. If you buy a round-trip ticket on July 1 for $660 and your friend provides a free ticket, then you can return the second half of your round-trip ticket to the airline, after paying a $50 penalty. In this case, your net travel cost will become $380. Develop a decision tree to determine how to minimize your expected travel cost. Find the optimal policy.

Sagot :

The optimal policy will be to book a round-trip ticket.

Based on the information given, there is a 30% chance that my best friend will be able to provide you with a free one-way ticket as a present. This will be represented on the decision tree as 0.3.

Therefore, the probability that I will not get a free ticket will be 0.7 which is calculated as 0.3 subtracted from 1.

The cost of booking the return ticket on August 1st will be:

= 350 + 370

= 720

In conclusion, the minimum expected travel is $576. The optimal strategy will be to book the round ticket now. An attachment has been attached for further understanding.

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