Jennifer Coggburn is choosing to buy a batch of $10,000 forms from one of the tw

Question

Jennifer Coggburn is choosing to buy a batch of $10,000 forms from one of the two suppliers: Supplier A and B. Supplier A charges $10,050 for Jennifer's order while Supplier B charges $10,000 for her order. Supplier A's overall nondefect rate is 90% (i.e., 90% of the time no forms are defective, whereas 10% of the time there are defects). Supplier B's overall nondetect rate is 85% (i.e., 85% of the time no forms are defective, whereas 15% of the time there are defects). If the forms turn out to be defective (10% of the time for Supplier A and 15% of the time for Supplier B), the number of defective forms from each of the suppliers is indicated in the following table: Number of Defective Forms Probability of Supplier A Probability of Supplier B 0.70 0.30 0.6 0.4 1,000 2,000 For Example, if she buys from Supplier A and the batch turns out to be defective, the probability that there are 1,000 defective forms is 0.70. When there are defective forms, Jennifer chooses one of the following options to fix them. The first option is to repair the defective items at a cost of $0.4 per defect forms. The second option requires re-working on the entire batch of 10,000 forms and this will cost her $500. Note: Supplier A's overall non-defect rate is 90% The probability of no defect is 0.9 - Probability that there are defects (either 1000 or 2000) is 0.1. Please use a decision tree analysis to determine which supplier Jennifer should choose to minimize the expected value of her cost by answering the following guestions: 1) What is Jennifer's expected cost if she chooses Supplier A and the forms turn out to be defective? 2) What is Jennifer's expected cost by choosing Supplier A? 3) Create a decision tree and solve

Explanation / Answer

Cost for choosing supplier A

=0.9*10,050+0.10*(cost if defective)

Cost for choosing supplier B

=0.85*10,000+0.15*(cost if defective)

Now cost if defective can be calculated by

For supplier A:

=0.7*0.4*1000+0.3*0.4*2000 + 10,050

=10,570

For supplier B:

=0.6*0.4*1000+0.4*0.4*2000 + 10,000

=10,560

=0.9*10,050+0.10*(10,570) = $10,102

Expected cost by choosing supplier B:

=0.85*10,000+0.15*(10,560) = $10,084

SO

Choosing supplier A and if not defective: $10,050 (90% chance)

Choosing supplier B and if not defective: $10,000 (85% chance)

Choosing supplier A and if defective: $10,570 (10% chance)

Choosing supplier B and if defective: $10,560 (15% chance)

Expected cost by choosing supplier A: $10,102

Expected cost by choosing supplier B: $10,084

Thus go ahead with Supplier B

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