You are a program manager on a $10M program and just learned that there is a disturbing likelihood that your product will not pass your customer's acceptance inspection. You have three choices: (1) pray, (2) invoke a $1M back-up program which is assured to pass inspection or (3) to employ a new test on your own, costing $0.3M, with the following performance: P(true positive) = 0.80 P(true negative) = 0.10; 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 Veitch diagram, the decision diagram, and all expected values.