Dan's Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $28.00. The publisher sells the book to Dan at $20.00. Dan will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Dan estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. How many copies should Dan order so as to maximize expected profit?

a. 1340

b. 1045

c. 1020

d. 1000

e. 1125

f. 1375

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umairfeb221999 umairfeb221999 · Answer 1 · 2020-03-03T15:53:09+01:00

Answer:

The answer is b as he should order 1045 copies to maximize his profits.

Explanation:

As

[tex]CR=\frac{C_{u} }{C_{o}+C_{u} }[/tex]

So,

Given :

[tex]C_{o} =20-14=6[/tex]

[tex]C_{u} =28-20=8[/tex]

Thus

[tex]CR=\frac{8 }{6+8 }[/tex]

[tex]=57.14\%[/tex]

thus [tex]Q^{*} =Norm.inu(0.5714,1000,250)[/tex]

[tex]=1045.0032[/tex]

≈ [tex]1045[/tex]

Which is option b.

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