Question

The data and scenario from this question follows into the next two questions, A plumbing company 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 first accompanying probability distribution for the proportion of defective faucets that it receives from this supplier. This supplier charges the company $33.00 per unit for this faucet. Although the supplier will replace any defects free of charge, the plumbing company managers figure the cost of dealing with the defects is about $4.00 each Proportion Defective Probability 0.01 0.4 0.03 0.3 0.07 0.2 0.16 0.1 Assuming that the plumbing company is planning to purchase 1,500 of these faucets from the supplier, what is the total expected cost to the plumbing company for the deal? The total expected cost is $ (ans 1). (Type the entire number, do not round. Do not include a comma)

Answer 1

Cost of faucet = $33.00
Cost for dealing with defect = $4.00
Number of units bought = 1500
Expected proportion of defect = 0.01*0.4 + 0.03*0.3 + 0.07*0.2 + 0.16*0.1 = 0.043
Total expected cost = 1500*33 + 1500*0.043*4 = $49758