Decision Analysis

A contractor is preparing to obtain aggregates for use on a job. A current borrow pit exists and is convenient. However, the contractor estimates that there is only a 55% chance that the quantity of useful aggregate is sufficient for the job. If she needs to plan and initiate another pit in the middle of the job, the cost associated with the start-up is estimated to be $800. There is no doubt that the large second pit will suffice.

A second alternative is to open a somewhat smaller second pit immediately, at a cost of $400. Between the two pits, there will be a 98% chance that sufficient aggregates will be available. But the small chance exists that even two pits will not suffice. The contractor will only entertain the choice of one or two pits and is prepared to pay another $300 if a very small third pit is needed.

Draw the decision tree, compute the expected monetary values, and define the optimal policy (i.e: Stay with one pit, or immediately open a second pit).