Question: Rossmore Brothers, Inc., sells plumbing supplies for commercial and residential applications. The company currently has only one supplier for a particular type of faucet. Based on historical data that the company has maintained, the company has assessed the following probability distribution for the proportion of defective faucets that it receives from this supplier:
Proportion Defective Probability
0.01 0.4
0.02 0.3
0.05 0.2
0.10 0.1
This supplier charges Rossmore Brothers, Inc., $29.00 per unit for this faucet. Although the supplier will replace any defects free of charge, Rossmore managers figure the cost of dealing with the defects is about $5.00 each.
a. Assuming that Rossmore Brothers is planning to purchase 2,000 of these faucets from the supplier, what is the total expected cost to Rossmore Brothers for the deal?
b. Suppose that Rossmore Brothers has an opportunity to buy the same faucets from another supplier at a cost of $28.50 per unit. However, based on its investigations, Rossmore Brothers has assessed the following probability distribution for the proportion of defective faucets that will be delivered by the new supplier:
Proportion Defective x Probability P(x)
0.01 0.1
0.02 0.1
0.05 0.7
0.10 0.1
Assuming that the defect cost is still $5.00 each and based on total expected cost for an order of 2,000 faucets, should Rossmore buy from the new supplier or stick with its original supplier?