Gulf Exploration Company operates drilling rigs in several locations in the Gulf of Mexico. The company does not produce oil itself but operates under contract to several major integrated oil companies. Its newest project is taking place on platform 105, from which shafts have already been drilled into a large producing field. Drilling is still taking place, even though the earlier wells are already producing crude for the parent company. Drilling superintendent Dick Dymond is evaluating alternative replenishment policies for supplying platform 105 for drill bits. These items are very expensive, and Gulf cannot afford to keep more than a nominal number of spares at the drilling site. Yet the cost of a drilling delay due to a worn or damaged bit can be huge, since the crew must still be paid and maintained during interruption in normal activity. Unlike a shore- based operation, resupply of drilling platform must be carefully orchestrated. It is typically done by sea, which is quite time consuming, or more quickly by air. In the case of drill bits, Mr. Dymond is considering two alternatives. The first policy is to keep just one working bit at the site, delivering a replacement by helicopter when it breaks. The second policy is to keep two bits at the site and to send replacements for all broken bits by boat only when at least one of them breaks. Mr. Dymond believes that there is only a 10% chance that a drill bit will break at any given day. A bit cannot be replaced on the same day that is breaks, and Helicopter delivery takes place the next day, so no lost production occurs in that case. A sea delivery takes one or more days, and only one boat can be dispatched at a time. Each day's lost production represents $10,000 in lost future profits, and the two delivery modes have identical costs. A production loss occurs whenever a bit breaks, which is assumed to happen near the beginning of a working day. When replacements are made or deliveries are received, they occur just before the day's drilling begins. Depending on the delivery mode chosen, one of the following states may apply at the beginning of any particular scheduled drilling day: A. No good bits. B. One good bit; no break yesterday. C. One good bit; a break yesterday. D. Two good bits; last replacement for one bit. E. Two good bits; last replacement for two bits. The process can be evaluated in terms of a Markov chain. Questions 1. Construct the two transition matrices for the two policies.

2.