University Toys has developed a brand new product linea series of Business Professor Action Figures (BPAFs) featuring likenesses of popular professors at the local business school. Management needs to decide how to market the dolls. One option is to immediately ramp up production and simultaneously launch an ad campaign in the university newspaper. This option would cost $1,000. Based on past experience, new action figures either take off and do well or fail miserably. Hence, the prediction is for one of two possible outcomestotal sales of 2,500 units or total sales of only 250 units. University Toys receives revenue of $2 per unit sold. Management currently thinks that there is about a 50 percent chance that the product will do well (sell 2,500 units) and a 50 percent chance that it will do poorly (sell 250 units). Another option is to test-market the product. The company could build some units, put up a display in the campus bookstore, and see how they sell without any further advertising. This would require less capital for the production run and no money for advertising. Again, the prediction is for one of two possible outcomes for this test market, namely, the product will either do well (sell 200 units) or do poorly (sell 20 units). The cost for this option is estimated to be $100. University Toys receives revenue of $2 per unit sold for the test market as well. The company has often test marketed toys in this manner. Products that sell well when fully marketed have also sold well in the test market 80 percent of the time. Products that sell poorly when fully marketed also sell poorly in the test market 60 percent of the time. There is a complication with the test market option, however. A rival toy manufacturer is rumored to be considering the development of Law School Professor Action Figures (LSPAF). After doing the test marketing, if University Toys decides to go ahead and ramp up production and fully market the BPAF, the cost of doing so would still be $1,000. However, the sales prospects depend upon whether LSPAF has been introduced into the market or not. If LSPAF has not entered the market, then the sales prospects will be the same as described above (i.e., 2,500 units if BPAF does well, or 250 units if BPAF does poorly, on top of any units sold in the test market). However, if LSPAF has been introduced, the increased competition will diminish sales of BPAF. In particular, management expects in this case to sell 1,000 if BPAF does well or 100 units if it does poorly (on top of any units sold in the test market). Note that the probability of BPAF doing well or doing poorly is not affected by LSPAF, just the final sales totals of each possibility. The probability that LSPAF will enter the market before the end of the test market is 20 percent. On the other hand, if University Toys markets BPAF immediately, they are guaranteed to beat the LSPAF to market (thus making LSPAF a nonfactor). Suppose that the test marketing is done. Use the Posterior Probabilities template to determine the likelihood that the BPAF would sell well if fully marketed, given that it sells well in the test market and then given that it sells poorly in the test market. Use Analytic Solver to develop and solve a decision tree to help University Toys decide the best course of action and the expected payoff. Now suppose that University Toys is uncertain of the probability that the LSPAFs will enter the market before the test marketing would be completed (if it were done). How would you expect the expected payoff to vary as the probability that the LSPAFs will enter the market changes? Generate a data table that shows how the expected payoff and the test marketing decision changes as the probability that the LSPAFs will enter the market varies from 0 percent to 100 percent (at 10 percent increments). At what probability does the test marketing decision change?