4. Acme Copier Supplies currently supplies copier paper from two warehouses. War

Question

4. Acme Copier Supplies currently supplies copier paper from two warehouses. Warehouse A ex- periences demands that are normally distributed with a mean of 30,000 cases per week and a standard deviation of 5,000 cases per week. Warehouse B experiences demands that are normally distributed with a mean of 30,000 cases per week and a standard deviation of 8000 cases per week. The two warehouses are resupplied only once per week (a) What is the probability that next week demand at warehouse A exceeds 32,500 cases? (b) What is the stock level required at warehouse A that will meet weekly demand 95% of the time? (c) What is the stock level required at warehouse B that will meet weekly demand 95% of the time? (d) Acme has the opportunity to consolidate the two warehouses into a single warehouse. Suppose that weekly demand at the two warehouses is independent. If they wish to stock a single warehouse so that weekly demand will be met 95% of the time, how much should they stock? Phom an inveastory point of view, does itmaesee to colidate the warebous (e) How does your answer to part d change if the correlation between demands at the two warehouses is +0.6875?

Explanation / Answer

We are allowed to do 4 subparts question at a time. Post again for more subparts of question.

a) P(A > 32500)

z = (32500 - 30000)/5000 = 0.5

P = 0.3086

b) 95% is two SD away

So, stock = 30000 + 5000 *2 = 40,000

c) stock = 30000 + 8000 *2 = 46,000

d) Combined Mean = 60,000

SD(X + Y) = sqrt[ Var(X + Y) ]  

Var (A + B) = 5000^2 + 8000^2 = 89000000

SD = 9433.98

Stock = 60,000 + 2* 9433.98 = 78868

Yes, it makes sense.

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