4. The local transit agency, an "expected profit maximizer", must decide whether to introduce a new fare card. The following information is gathered during a meeting: . The marketing vicepresident has defined two possible outcomes; either the public will accept the fare card or it will not. She believes the probability of acceptance is 0.1. . The cost engineers believe that if the fare card is marketed and accepted, the agency will net $100,000 annually. If the fare card is rejected, however, the company will suffer a net annual loss of $20,000. If the agency decides not to market the fare card, it wil neither accrue more cost nor make any profit. (a) What strategy would you recommend for this case? (b) What is the maximum amount that should be paid for a market research study on the public's perception of the fare card? A consultant for the agency proposes conducting a market research study. Based on histories of similar tests, she estimates that the sample population would not accept the fare card with a probability of 0.2, when in fact the fare card would be accepted by the general public. She also believes that one time in forty the fare card would be accepted by the public when the test group rejects it. Finally, she informs the agency that the probability of acceptance when the test group accepts is 0.4. (c) Sketch the decision tree and calculate the maximum amount that should be paid for the proposed test