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Quantitative Methods - should a plane go commercial probability

Management is considering going live with a new product that research believes is promising. Engineering estimates that if a $300,000 pilot plant is build there is a 0.75 chance of a high yield versus the alternative of a low yield. If the pilot plant shows a high yield they believe there is a probability of 0.8 that the commercial plan will also have a high yield. If the pilot plan shows a low yield, there is only a .15 chance that the commercial plant will have a high yield. The company stands to make $12,150,000 if the commercial plant has a high yield while a loss of $1,510,000 is projected if the yield is low. There is some disagreement as to whether Engineering's pilot plant will be a reliable model for the scaled up commercial plant. What is your conclusion about the value that will be obtained from the pilot plant and whether the company should even entertain the idea of going commercial at all?

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P(Pilot High Yield) = 0.75 P(Pliot Low Yield)=1-0.75=0.25
P(Commercial high yield / Pilot High Yield) = 0.80 P( Commercial low yield / Pilot High Yield) = 1-0.80=0.20
P(Commercial high yield / Pilot low Yield) = 0.15 P( Commercial low yield / Pilot low Yield) = 1-0.15=0.85

The expected profits if management goes without pilot project
=P(High Yield)*Payoff with high yield + P(Low Yield)*Payoff with low yield

The expected profits if management takes up pilot project:
There are two outcomes: high yield and low yield
With high yield the expected profits ...

Solution Summary

The solution uses quantitative methods to determine if it is worth while for a pilot to go into commercial flying.