6. Two professors at a nearby university want to co-author a new textbook in either economics or statistics. They feel that if they write an economics book, they have a 50 percent chance of placing it with a major publisher, and it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80 percent chance of placing it with a smaller publisher, with ultimate sales of 30,000 copies. On the other hand, if they write a statistics book, they feel they have a 40 percent chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50 percent chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. a. Construct a decision tree for this problem. b. What is the probability that the economics book would wind up being placed with a smaller publisher? c. What is the probability that the statistics book would wind up being placed with a smaller publisher? d. What is the expected value for the decision alternative to write the economics book? e. What is the expected value for the decision alternative to write the statistics book? f. Which decision alternative should be selected and what is the expected value for this (the optimum) alternative