Show step by step. A magazine editor wanted to publish a hardcover edition of a selection of photographs from his magazine. The photo edition would be sold primarily by mail order to people whose names appeared in the magazine's directory. The directory not only included subscribers, but also people considered potential subscribers. The management believed that a large number of copies could be sold, due to the reputation of the magazine and the excellent reviews that the photographic sections had received when they were first published in the magazine. What's more, many people had sent letters to propose that an edition of this type be presented. Money had already been invested in the edition when the photographs and text for the magazine were prepared. However, it was estimated that another $10,000 would be spent. In addition, the cost of designing and printing the advertising material and mailing it was estimated to be $250,000. The magazine's directory included nearly two million names (some of which, of course, were duplicates). It was proposed to make two shipments, with a cost per name of five cents for mail. About $50,000 would also be invested in the development of advertising material. The variable manufacturing cost of the book would be two dollars per copy. The sale price would be set at three dollars. The management had not yet decided about the publishing project, due to the high initial costs. The best estimates were around 250,000 copies sold. Management believed that there was a 70% probability that sales would be between 200,000 and 300,000 copies. Management was opposed to abandoning the project, as the edition could have a high prestige value. Therefore, the possibility of carrying out a market study was considered before making the final decision. It would be quite simple to select a sample of people from the magazine's directory and evaluate the acceptance of the edition. Postage costs and other variable costs totaled 25 cents per individual in the sample. However, special advertising material had to be printed, at a cost of $13,000, regardless of the number of people in the sample. A sample of 2000 people was considered adequate. The company's statisticians estimated that the standard error of the mean for a sample of 2,000 people would be 10,000 books. a) Based on the information above, what are the expected benefits from the publication of this book? If you don't take into account additional benefits, such as prestige value, should the book be published? What is the expected value of perfect information (VEIP)? b) What is the expected value of the sample information (VEIM)? c) What is the expected net gain from sampling? Should sampling be carried out?