Petro Enterprises is a small oil exploration business. They have a nontransferable short-term option to drill on a certain plot of land. Two recent dry holes have depleted Petro's net liquid assets to $130,000. The president must decide whether Petro should exercise its short-term option or allow it to expire. (It will expire in two weeks if drilling is not commenced by then.) The president has the opportunity of paying for a seismic test run in the next few days, which could help determine if it is worth drilling. To conserve capital and maintain flexibility, Petro subcontracts all drilling and seismic tests. It can have the seismic test performed on short notice at overtime rates for a fixed fee of $30,000 and the well can be drilled for a fixed fee of $100,000. If oil is found, Petro must decide whether to develop the oil field itself or sell the rights. A large oil company has agreed that if Petro drills and discovers oil, it will purchase all of Petro's rights for $400,000.

The company's geologist has examined the geology of the region and states that there is a 0.55 probability that if a well is sunk, oil will be discovered. Data on the reliability of the seismic test indicate that if the test is favourable, the probability of finding oil will increase to 0.85 but that if the test is unfavourable, it will fall to 0.1. The geologist has computed that there is a 0.6 probability that the result will be favourable if the test is made.

Unfortunately, if oil is discovered, it is not possible to know the extent of the find before the decision as to whether or not to sell the rights to the land expires. Past experience suggests that if oil is found, there is a 0.2 probability that it is a small reservoir, 0.7 probability that it is a medium reservoir and 0.1 probability that it is a large reservoir. Petro estimates its profits (not including costs associated with exploration) from developing the oil field itself to be $200,000 if the reservoir discovered is a small one, $350,000 if it is a medium reservoir and $800,000 if it is a large one.

The question:

 

Provide the decision tree and using a Decision Tree, determine Petro's best policy in terms of whether or not to take advantage of the seismic test and also whether or not to develop or sell the rights if oil is found.