As the lead systems engineer in an automotive company, you need to make a critical decision: whether to outsource the design and maintenance of your powertrain or to keep that responsibility in-house. While making that decision, there is uncertainty associated with how often the powertrains will fail: either rare or often. If you decide to outsource the design and maintenance, you pay a fixed contract rate of $20M to an external company, which delivers the design and takes the responsibility of the maintenance service under a warranty regardless of how often the vehicle powertrain fails. If you decide to keep the design and maintenance in-house, your company must decide whether to use the existing design with minimal changes or to invest on a new design. o The existing design is difficult to maintain and cheap to develop. If the failures occur often, it will cost $25M in the long run for the design and maintenance, and if the failures are rare, it will cost $15M. The new design will be easier to maintain but costly to develop. If the failures are often, it will cost $23M in the long run; and if the failures are rare, it will cost $16M. Based on your rough estimates, the failures will be often with a probability of 0.4, and it will be rare with a probability of 0.6.

Find the maximum amount you should pay to obtain perfect forecasts about the failure rates in the future, i.e., find the expected value of perfect information.