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 of defective units in a lot Probability
0.05 0.50
0.10 0.25
0.25 0.15
0.50 0.10
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.
Input Data
Number of units in a lot 1000
Cost of purchasing a lot $30,000
Cost of repairing a defective unit in a lot $20
Cost of purchasing supplier's guarantee policy (per lot) $1,000
Selling price for a unit of the component $45
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