21 Pipeline Construction Model. The following exercise is a variation of the classical “machine setup” problem. The installation of an oil pipeline that runs from an oil field to a refinery requires the welding of 1,000 seams. Two alternatives have been specified for performing the welding: (1) use a team of ordinary and apprentice welders (B-team) only, or (2) use a team of master welders (A-team) who check and rework (as necessary) the welds of the Bteam.
If the first alternative is chosen, then it is estimated from past experience that 5% of the seams will be defective with probability 0.30, 10% will be defective with probability 0.50, or 20% will be defective with probability 0.20. However, if the B-team is followed by the A-team, then a defective rate of 1% is almost certain.
Material and labor costs are estimated at $400,000 when the B-team is used strictly, whereas these costs rise to $530,000 when the A-team is also brought in. Defective seams result in leaks that must be reworked at a cost of $1,200 per seam, which includes the cost of labor and spilled oil but ignores the cost of environmental damage.

a. Determine the optimal decision and its expected cost. How might environmental damage be taken into account?

b. A worker on the pipeline with a Bayesian inclination (from long years of wagering on the ponies) has proposed that management consider x-ray inspections of five randomly selected seams following the work of the B-team. Such an inspection would identify defective seams, which would provide management with more information for the decision on whether to bring in the A-team. It costs $5,000 to inspect the five seams.
Financially, is it worthwhile to carry out the inspection? If so, then what decision should be made for each possible result of the inspection?