Discuss the construction of a decision tree for the engineer in the following situation. Which is the best action-state pair and how might utilities and probabilities be estimated? Make some reasonable guesses for numerical values. A reinforced-concrete school building is under construction, and questions about concrete strength have arisen during construction. The contract cost of the entire structure is $2,161,713, and it is estimated that replacement of the concrete in question will cost $300,000 to $400,000. The superstructure of the two- and three-story building is specified to contain 4 percent of entrained air with a design strength of 3500 psi. Tests show up to 10 percent air, and tests made on concrete cylinders and 90 cores show a mean strength of 2100 psi when projected to a 28-day strength. The situation is complicated by the results of load tests. In 16 tests using a superimposed load of 1.5 times the design live load plus half the dead load on the beams and slabs, the structure showed no signs of distress. Replacement involves perhaps a year's delay in the completion of the badly needed structure. Acceptance of the present structure involves assumption of liability in the event of poor future performance. The decision is complicated by the unknown relationships between beam capacity and concrete cylinder strength, particularly with under reinforced sections, and by the likelihood that the entire specified design strength is not needed in most of the structure. Note that the decisive value is to be received at some unknown future time. Thus value to a well established firm may differ from the value to an office that will cease operations in the near future.