The purchasing agent for a microcomputer manufacturer is currently negotiating a purchase agreement for a particular electronic component with a given supplier.

This component is produced in lots of 1000, and the cost of purchasing a lot is $30,000. Unfortunately, past experience indicates that this supplier has occasionally shipped defective components to its customers.

Specifically, the proportion of defective components supplied by this supplier is described by the probability distribution given in the file P10_66.xlsx.

Although the microcomputer manufacturer can repair a defective component at a cost of $20 each, the purchasing agent is intrigued to learn that this supplier will now assume the cost of replacing defective components in excess of the first 100 faulty items found in a given lot. This guarantee may be purchased by the microcomputer manufacturer prior to the receipt of a given lot at a cost of $1000 per lot. The purchasing agent is interested in determining whether it is worthwhile for her company to purchase the supplier’s guarantee policy.

a. Create a payoff table that specifies the microcomputer manufacturer’s total cost (in dollars) of purchasing and repairing (if necessary) a complete lot of components for each possible decision and each outcome with respect to the proportion of defective items.

b. Use PrecisionTree to identify the strategy that minimizes the expected total cost of achieving a complete lot of satisfactory microcomputer components.

c. Perform a sensitivity analysis on the optimal decision and summarize your findings. In response to which model inputs is the expected earnings value most sensitive?