A distributor of computer parts purchases a specific component from a supplier in lots of 1000 units. The cost of purchasing a lot is $30,000. The supplier is known to supply imperfect lots. In other words, a lot received by the distributor may contain defective units. Historical data suggest that the proportion of defective units in a lot supplied by this supplier follows the following probability distribution:

Proportion Probability

.05 .5

.10 .25

.25 .15

.5 .10

The distributor inspects the entire lot for defective units before selling the units to PC repair shops at a price of $45 per unit. The inspection process is error-proof so all defective units in a lot are detected and replaced by the distributor. It costs $20 for the distributor to replace a defective unit. The distributor has recently learned that the supplier offers a guarantee policy through which the supplier will assume the cost of replacing defective units in excess of the first 100 faulty units found in a given lot at no cost.[This means that the first 100 defective units found in a lot are replaced by the distributor for $20 per unit; however, all additional defective unit (if any) found in a lot are replaced by the supplier at no cost to the distributor.] This guarantee policy may be purchased by the distributor prior to the receipt of a given lot at a cost of $1000 per lot. The distributor wants to determine whether it is worthwhile to purchase the supplier's guarantee policy.

• Show a decision tree by usingPrecisionTree.
• Make a recommendation: What should the distributor do, using EMV as the decision-making criterion? Why?
• Perform sensitivity analysis:Perform aone-waysensitivity analysis usingPrecisionTreeon the optimal decision by letting the cost of replacing a defective unit vary from $10 to $30 in 11 steps and the cost of purchasing the supplier's guarantee policy vary from $400 to $1600 in 7 steps. Comment on your findings.