Starting with the finished version of Example $7\mathrm{.}2,$ change the decision criterion to "maximize expected utility," using an exponential utility function with a risk tolerance of $$5$ million. Display certainty equivalents on the tree.

a$.$Keep doubling the risk tolerance until the company's best strategy is the same as with the EMV criterion$$continue with development and then market if successful.

The risk tolerance must reach Select$$20,000,000$$$80,000,000$$$160,000,000$$$320,000,000$$$1,280,000,000$Item $1$ before the risk$-$averse company acts the same as the EMV$-$maximizing company.

b$.$With a risk tolerance of $$320,000,000,$ the company views the optimal strategy as equivalent to receiving a sure $ $,$ even though the EMV from the original strategy $($with no risk tolerance$)$ is $ $.($Round your final answer to the nearest $$100,$ if necessary.$)$