Peter Equipment Toys must decide the course of action to follow in promoting a new whistling yo-yo. Initially, management must decide whether to market the yo-yo or to conduct a test marketing program. After test marketing the yo-yo, management must decide whether to abandon it or nationally distribute. A national success will increase profits by $500,000, and a failure will reduce profits by $100,000. Abandoning the product will not affect profits. The test marketing will cost Peter Equipment Toys a further $10,000. If no test marketing is conducted, the probability for a national success is judged to be 0.45. The assumed probability for a favorable test marketing result is 0.50. The conditional probability for national success given favorable test marketing is 0.80; for national success given unfavorable test results, it is 0.10. Construct the decision tree diagram and perform backward induction analysis to determine the optimal course of action if a net change in profits is the expected payoff.