An engineer who works for a company that produces equipment for the food-processing industry has been asked to consider the development of a new type of processor and to make a recommendation to the company's board. Two alternative power sources could be used for the processor, namely gas and electricity, but for technical reasons each power source would require a fundamentally different design. Resource constraints mean that the company will only be able to pursue one of the designs and, because the processor would be more advanced than others that have been developed, it is by no means certain that either design would be a success. The engineer estimates that there is a 70% chance the electricity-powered design would be successful and only a 60% chance that the gas-powered design would be successful. If either design fails, then the company would still consider modifying the design, although this would involve more involvement and would still not guarantee success.

If the electric-powered design is selected and it's a success, then the company is expected to earn $14 million. If the electrical design fails, the engineer estimates that the probability that it could be successfully modified is only 60%. If the modification is a success, then the company will earn $8 million. However, if it's a failure, then the firm will lose $9 million. On the other hand, if the electrical design is not a success and the company decides to abandon the project, then this will cost the company $5 million.

If the gas-powered design is selected and it's a success, then the company is expected to earn $17 million. If the gas design fails, the engineer estimates that the probability that it could be successfully modified is 75%. If the modification is a success, then the company will earn $12 million. However, if it's a failure, then the firm will lose $14 million. On the other hand, if the gas design is not a success and the company decides to abandon the project, then this will cost the company $8 million.

a) Draw a complete decision tree for this problem. Clearly present the decision and event nodes, the associated probabilities, and the payoffs.

b) What should the management do to achieve the highest expected payoff?