Question

This question has three parts.

Part 1.

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 $ ______. (Type the entire number, do not round. Do not include a comma)

Part 2)

The data and scenario from part of this question relates to the previous question.

Suppose that the plumbing company has an opportunity to buy the same faucets from another supplier at a cost of $ 32.00 per unit. However, based on its investigations, the company has assessed the second accompanying probability distribution for the proportion of defective faucets that will be delivered by the new supplier (see below). Assuming that the defect cost is still $4.00 each and based on total expected cost for an order of 1,500 faucets.

Proportion Defective	Probability
0.01	0.1
0.03	0.1
0.07	0.7
0.16	0.1

The total expected cost is $ ______ . (Type the entire number, do not round. Do not include a comma)

Part 3)

Because the expected cost for the new supplier is [more OR less] than that for the original
supplier, the company should buy from the [new OR original]   supplier.

Answer 1

Cost of faucet = $33.00

Cost for dealing with defect = $4

a) Number of units bought = 1000

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

b) Total expected cost from new supplier =

= 1500*32 + 1000*4*[0.01*0.1 + 0.03*0.1 + 0.07*0.7 + 0.16*0.1] = $48276

Since the total expected cost for the new supplier is $48276 which is less than that for the original supplier, The company should buy from the new supplier.