You are a program manager on a $10M program and just learned that there is a disturbing likelihood that your productwill not pass your customer's acceptance inspection. You have three choices:

1. Do Nothing

2. Invoke a $1M backup program which is assured to pass inspection or

3. Employ a new test-costing $0.3M of your own money with the following performance: p(true positive) = 0.8; p(true negative) = 0.1; p(false positive) = 0.07; p(false negative) = 0.03 (If you fail this test, of course you can still invoke the back-up program.)

What is your most rational decision? Show the decision diagram and all expected values.