A company has developed a new product. It needs to decide whether or not to product test and market test before launch, and has been advised that, even though these processes do cost money, they increase the likelihood of success for the product. (Note that it has been agreed within the company that you can only market test a product once it has passed product testing. If a product fails either test it is regarded as worthless). You have been able to obtain details of the costs of these testing processes, together with historical data which suggest how much the likely success of the product is enhanced by successful testing. Launching the product will cost 300,000 and the estimates of profit are as follows:

Highly successful	=	2,000,000
Moderately successful	=	1,000,000
Low level success	=	500,000
Failure	=	100,000

The historical data that has been collected gives the following results:

	No testing	Product testing	Product testing & market testing
High success	0.1	0.1	0.2
Medium success	0.2	0.4	0.45
Low success	0.4	0.4	0.3
Failure	0.3	0.1	0.05

Product testing costs 100,000 and Market testing costs 100,000. Should the product fail either of these tests it is abandoned. The probability of passing product testing is 0.8 and the probability of passing market testing is 0.9. The alternative to this process is to sell the product design for

500,000.

1. Construct a decision tree and write a very brief report advising the company on its best course of action.

2. What would be the best decision if the profit from the highly successful product were estimated to be 3,500,000 rather than 2,000,000?

3. Discuss your solution to part b) by listing all the possible outcomes that could happen if the company is to follow the recommendation suggested by your solution.

Refer to the settings specified under part b) once again and imagine that you were the decision maker of this company. What would you really decide to do? Would you follow the recommendation obtained by the decision tree model? Why yes or why not?

For reference of decision tree

ecision tree showing all the labels, probabilities and consequence values: 0.842 8000 6 P nc 3 o 40000 0.158 0.842 O 18000 pc 0.38 Q 7 nc 2 o 32000 0.158 0.129 8000 order survey 0.62 8 P nc pnc 4 40000 0.871 0.129 o 18000 1 9 nc 32000 0.871 0.4 8000 do not order survey 10 nc 5 0.6 o 40000 0.4 Q o 18000 11 nc o 32000 0.6 ecision tree showing all the labels, probabilities and consequence values: 0.842 8000 6 P nc 3 o 40000 0.158 0.842 O 18000 pc 0.38 Q 7 nc 2 o 32000 0.158 0.129 8000 order survey 0.62 8 P nc pnc 4 40000 0.871 0.129 o 18000 1 9 nc 32000 0.871 0.4 8000 do not order survey 10 nc 5 0.6 o 40000 0.4 Q o 18000 11 nc o 32000 0.6