Expert Plumbers sells plumbing supplies for commercial and residential applicati

Question

Expert Plumbers sells plumbing supplies for commercial and residential applications The company currently has one supplier for a certain type of faucet. Based on historical data that the company has maintained, the company has determined the following probability distribution for the proportion of defective faucets that it receives from this supplier: Probability 0.4 0.3 0.2 0.1 Proportion Defective 0.01 0.02 0.05 0.10 This supplier charges Expert Plumbers $29.00 per unit for this faucet. Although the supplier will replace any defect free of charge, Expert Plumber managers figure that the cost of dealing with defects is about $5.00 each Find the expected proportion of defective faucets from this supplier. Suppose that Expert Plumbers is planning to purchase 2,000 faucets. What will be the total expected cost (include the cost of the faucets and the cost to deal with defective faucets) Suppose that Expert Plumbers has an opportunity to purchase faucets from another supplier at a cost of S28.50 per unit. However, based on its investigations, Expert has determined the following probability distribution for the proportion of defective faucets for the new supplier. Proportion DefectiveProbability 0.1 0.1 0.7 0.1 0.01 0.02 0.05 0.10 Assuming that the defect cost is still $5.00 each and based on a total order of 2,000 faucets, should Expert buy from the new supplier or stick with its original supplier?

Explanation / Answer

1. Expected proportion of defects = 0.01x0.4 + 0.02x0.3 + 0.05x0.2 + 0.10x0.1 = 0.030

2. Total expected cost = 2000x29 + 2000x0.03x5

= $58300

3. Total cost from the second supplier = 2000x28.5 + 2000 (0.01x0.1 + 0.02x0.1 + 0.05x0.7 + 0.1x0.1)x5

= 57000 + 2000x0.048x5

= $57480

Total cost is less with new supplier and hence, the expert should buy from the new supplier

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