A part of an aircraft engine can be given a test before installation. The test has a 75% chance of revealing a defect if it is present, and the same chance of passing a sound part. Whether or not the part has been tested it may undergo an expensive rework operation which is certain to produce a part free from defects. If a defective part is installed in the engine the loss is L. If the rework operation costs L/5 and one in eight parts are initially defective, calculate the most you should pay for the test and determine all the optimum decisions. Show your thinking in a decision tree.