A large reinforced-concrete building is to be constructed on very poor foundation material. The building is 60 ft wide, 200 ft long, and 6 stories in height. Two basic foundation alternatives are friction piles or some type of raft foundation. A differential settlement on the order of 3 in. can be expected to involve legal problems with the client, since you have already indicated that the site is adequate for the proposed construction. Routine tests and studies indicate that a pile foundation can be expected to show long-term differential settlements of up to 3 in. Odds cannot be quoted that the settlement will not be larger, but it is unlikely. The odds are approximately even that the differential settlement will be less than 1 in., approximately 4 to 1 that it will be less than 2 in., and perhaps approximately 1 in 100 that it will be approximately 3 in. The cost of a pile foundation is so large that it is "even money" that the client will abandon the job if this design is suggested. Use discrete states and note that the measures of likelihood must be normalized. Studies for a raft foundation indicate that a relatively flexible slab coupled with rock surcharge around the building will be within the cost estimates. The odds are more or less even that the differential settlement will be less than 2 in. and approximately 10 to 1 that it will be less than 3 in. If the settlement is too large, the client will take legal action against you; you expect the cost to you will be $1,000 or $10,000 with equal likelihood. Your profit on the job will probably be $3,000, providing that it goes to completion.
(a) Set up the decision tree for this decision and determine the optimum action.
(b) If the client now says he will not pay your usual fee, determine the offered fee level below which you would sue him for the original fee assuming that the cost of collection is $500. Assume that the client will be required to pay you $3,000 and normal engineering costs are not influenced by the legal problems. Note that this type of operation does not imply that you will not be offered future jobs. In fact, if you reduce your fee (under pressure), you can expect to receive future jobs (with attendant fee difficulties). Note that you could hedge against such problems by asking for more than you expect in the initial negotiations.