A company has developed a new type of mosquito repellant

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A company has developed a new type of mosquito repellant. The technical success is clear, but as with any new product the commercial success is risky. Because of this, they would sometimes test-market a product first, and then make a decision about national marketing after the test-market results had come in; at other times they would proceed directly to national marketing. On some occasions, they would abandon the product without even test-marketing it.

The test-marketing would cost about $600,000. If successful (probability 0.4) there would be revenues of $200,000; if unsuccessful the revenues would only be $50,000. Should the test market be successful, a follow-up national campaign at a cost of $2,500,000 would have a 70% chance of success with a revenue of $9,000,000, otherwise it would be a failure with a revenue of $750,000. Should the test market be unsuccessful, a follow up national campaign would have only a 0.2 chance of success (with the same cost, and the same revenues for success and failure). A national campaign not preceded by a test campaign would have a 45% chance of success. It would cost $3,000,000, and would produce a revenue of $9,500,000 if successful, but only $875,000 otherwise.

(a) Draw and solve a decision tree for the situation (using payoff nodes where appropriate), and state the recommendation clearly.

(b) If the $3,000,000 figure in the last paragraph were changed to $4,000,000, what would be the revised recommendation?