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​Bloom's Jeans is searching for new​ suppliers, and Debbie​ Bloom, the​ owner, has narrowed her choices to two sets. Debbie is very concerned about supply​ disruptions, so she has chosen to use three suppliers no matter what. For option​ 1, the suppliers are​ well-established and located in the same country. Debbie calculates the​ "unique-event" risk for each of them to be 5​%. She estimates the probability of a nationwide event that would knock out all three suppliers to be 2.2​%. For option​ 2, the suppliers are newer but located in three different countries. Debbie calculates the​ "unique-event" risk for each of them to be 21​%. She estimates the​ "super-event" probability that would knock out all three of these suppliers to be 0.3​%. Purchasing and transportation costs would be ​$950 comma 000 per year using option 1 and ​$960 comma 000 per year using option 2. A total disruption would create an annualized loss of ​$480 comma 000.a) the probability that all three suppliers will be disrupted using option 1 is your response to five decimal places).​b) the probability that all three suppliers will be disrupted using option 2 is your response to five decimal places).​c) the total annual purchasing and transportation cost plus expected annualized disruption cost for option 1 is your response to the nearest whole number).​d) the total annual purchasing and transportation cost plus expected annualized disruption cost for option 2 is your response to the nearest whole number).​e) based on the total annual purchasing and transportation cost plus expected annualized disruption cost,(option 1 or option 2) seems best.

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Answer:

Part a: The required probability for option 1 is is 0.02212.

Part b: The required probability for option 2 is is 0.01223.

Part c: The total cost for option 1 is $960617.6

Part d: The total cost for option 2 is $965870.4

Part e: Option 1 is the better option with the total cost of $960617.6  as compared to $965870.4 for option 2.

Explanation:

Part a:

For the option A

Probability of an event which can knockdown suppliers nation wide is given as

P(U)=5%

Probability of the super event such that knock out all three of these suppliers is as

P(S)=2.2%

So the required probability is given as

[tex]P(X) = P(S) + (1 - P(S)) \times P(U)^3\\P(X) = 2.2\% + (100\% - 2.2\%)(5\%)^3\\P(X) = 0.022 + (0.978)(0.05)^3\\P(X) = 0.02212\\[/tex]

So the required probability is 0.02212.

Part b:

For the option B

Probability of an event which can knockdown suppliers nation wide is given as

P(U)=21%

Probability of the super event such that knock out all three of these suppliers is as

P(S)=0.3%

So the required probability is given as

[tex]P(X) = P(S) + (1 - P(S)) \times P(U)^3\\P(X) = 0.3\% + (100\% - 0.3\%)(21\%)^3\\P(X) = 0.003 + (0.997)(0.21)^3\\P(X) = 0.01223\\[/tex]

So the required probability is 0.01223.

Part c:

The Cost is given as

Purchase and Transportation Cost is as P_C=$950,000

Annualized Losses is as AL=$480,000

Also the probability as calculated in part a is as P(X)= 0.02212

So the total cost is given as

[tex]P_T=P_C+AL*P(X)\\P_T=\$950000+\$480000*0.02212\\P_T=\$960617.6[/tex]

So the total cost for option 1 is $960617.6

Part d:

The Cost is given as

Purchase and Transportation Cost is as P_C=$960,000

Annualized Losses is as AL=$480,000

Also the probability as calculated in part a is as P(X)= 0.01223

So the total cost is given as

[tex]P_T=P_C+AL*P(X)\\P_T=\$960000+\$480000*0.01223\\P_T=\$965870.4[/tex]

So the total cost for option 2 is $965870.4

Part e

On the basis of the total cost, as the value is less for option 1 thus option 1 is the better option with the total cost of $960617.6  as compared to $965870.4 for option 2.

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