Tim wishes to buy a used van, and decides to buy a three-year-old VW Adventurwagen. He surveys used van dealers in the area, and finds one that sells vans for $5500. The dealer, however, offers to sell him one particular van for $5000. Just before closing the deal. Tim overhears a conversation with the dealer. It turns out that 20% of the vans in his lot were "lemons" and the rest were "peaches." The dealer repaired all the vans in the lot, except for the van he has now offered to Tim. Lemons have exactly 6 defects in the 10 main systems in the van, and the peaches have only 1. The cost for the repairs equals $200 for a single defect, and s1000 total for all defects. All defects will appear at the same time, soon after Tim buys the van. Treat Tim as risk neutral over the prospects in this problem. Tim can take the van to a mechanic, but only for one hour. The mechanic can run one of the following three testing programs in one hour. Test the steering system alone for $45. Test the fuel and electrical systems for a total of S65. Two-test sequence: test the transmission at a cost of $50. with the option to test the differential at a cost of $20 after seeing the results of the transmission test. Note: Create quality distinctions for the following problems, or else the diagram and the tree will be huge and ugly. Just because I use a distinction in the problem statement does not mean you have to use the same distinction. g. Draw a decision diagram representing Tim's decision to purchase a test. h. Draw a decision tree representing Tim's decision to purchase a test. Using this tree, find Tim's best altermative and Tim's CE for his decision.