Starting with the finished version of Example $6\mathrm{.}2,$ change the decision criterion to "maximize expected utility," using an exponential utility function with risk tolerance $$5,000,000.$ 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

$$160,000,000$

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 $

$100,000$

$,$ even though the EMV from the original strategy $($with no risk tolerance$)$ is $

$100,000$

$.($Round your final answer to the nearest $$100,$ if necessary.$)$