Larrys Bakery operates a chain of ten high-end bakeries. Larry, the owner of these amazing bakeries, is looking at two options to increase his revenues throughout his chain of bakeries.

The first option is to launch a loyalty card. Doing this would cost Larry $500,000. The probability that this would result in high sales is 0.6, which means the probability it would result in low sales is 0.4. If high sales are generated from this option, Larry can expect to see additional revenues of $1,000,000. If low sales are generated from this option, Larry can expect to see additional revenues of only $750,000.

The second option Larry has is to cut the prices throughout his bakeries. Doing so would cost him $300,000. The probability that this would result in high sales is 0.8. If doing this results in high sales, Larry can expect to see additional revenues of $800,000. If it results in low sales, he can expect to see additional revenues of only $500,000.

Larry obviously has a tough decision ahead of him. He is currently leaning towards launching a loyalty card, yet the probabilities scare him. Larry can make his decision slightly easier by hiring a private bakery investigator. This investigator would go out and non-creepily talk with all of Larrys customers, and ask them if they would like the loyalty card. This option comes at a price though. Larry would have to pay this mysterious investigator $75,000 for him to do his job. The investigator would come back to Larry with a satisfactory or unsatisfactory decision. A satisfactory decision would mean that the probability of high sales given the launch of a loyalty card, would be 0.9, while an unsatisfactory decision would mean the probability of low sales would be 0.7, given the launch of a loyal card. The likelihood of the investigator providing a satisfactory decision if 0.6.

You need to decide which of these options you should go with, if either. Remember, your goal is to maximize profit. If you do decide that one of these options is worthwhile, should you hire the mysterious, private bakery investigator to not creepily talk to your customers?

Develop a decision tree to find the best decision strategy for Larry, based on expected monetary value. What is the optimal strategy? What is the corresponding expected monetary value yielded from this tree?