3) An engineer has been called upon to judge the adequacy of an existing structure. Complete plans are available and preliminary computations show that the steel reinforcing is ample. Site inspection raises question of quality of concrete and construction of a number of long-span slabs because of large deflections. The engineer's fee of $1,000 is guaranteed independent of his report conclusions. The owner has stated that he desires one of three reports based on strength according to code. Structure is unsafe. Structure is safe for office loading, 2.5 kN/m. Structure is safe for light storage load, 6.0 kN/m. The engineer's prior probabilities of capacity are State (live load capacity in kN/m) Probability 1.0 0.2 2.5 0.3 4.0 0.2 5.5 0.2 7.0 0.1 The owner believes very strongly that the structure is safe for light storage. If the engineer reports that the structure is unsafe, he faces loss of future jobs for the owner with a present worth of $5,000, whether he is correct or not. If he reports that the structure can be used for offices only, he has a probability of only 0.20 of receiving the desired jobs. If the engineer reports that the structure is safe for light storage, the future jobs are assured, provided that the performance is adequate. The total cost of reporting "adequate for office loading" and finding 0 < 2.5 kN/m is $5,000; the cost of being wrong (0 < 6.0 kN/m) with a report "adequate light storage" is $10,000. Construct the decision tree for this situation. Is the fee of $1,000 important to the decision? Why?