Question

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

Answer 1

Answer:

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

Explanation:

As

$CR=\frac{C_{u} }{C_{o}+C_{u} }$

So,

Given :

$C_{o} =20-14=6$

$C_{u} =28-20=8$

Thus

$CR=\frac{8 }{6+8 }$

     $=57.14\%$

thus      $Q^{*} =Norm.inu(0.5714,1000,250)$

                 $=1045.0032$

                  ≈ $1045$

Which is option b.