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The demand of a product is normally distributed with mean 1,000 and standard deviation 400. The...

The demand of a product is normally distributed with mean 1,000 and standard deviation 400. The overage cost is $30 and underage cost is $50.

a.) What is the optimal order quantity?

b.) What is the expected profit?

c.)The manager decided to order just the mean demand. What is the expected profit under this policy?

business   Operations-Management   
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Answer #1

a.

P(R<Q*) = Cu/ (Cu+Co) = 50/(50+30) = 0.625

NORMSINV(0.625) gives 0.318639

Q* - mean / st. dev = 0.318639

Q* = 0.318639* 400 + 1000

Q* = 1127.4556

Q* = 1127

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