Question

The first edition hardcover of a new book by a popular writer has a demand which is normally distributed with an average of 5 million and a standard deviation of 1 million. The production and transportation costs per hardcover are $12, and the sale price in bookstores is $30. When the paperback version comes out, the hardcover books go on sale for $7.50. How many hardcovers should be produced? Group of answer choices

A. 6.00 million

B. 5.00 million

C. Approximately 5.84 million

D.Exactly 5.80 million

Answer 1

Answer: C (Approximately 5.84 million)

Rationale:

Selling of hardcover (S.P.) = $ 30

Cost Price of handcover (C.P.) = $ 12

Salvage Value of hardcover (S.V.) = $ 7.5

Underage Cost (Cu) = S.P. - C.P.

Underage cost (Cu) = $ 30 - $ 12

Underage Cost (Cu) = $ 18

Overage cost (Co) = C.P. - S.V.

Overage Cost (Co) = $ 12 - $ 7.5

Overage cost (Co) = $ 4.5

Service level = Cu/ (Cu+Co)

Service level = 18/ (18+4.5)

Service level = 0.8

*Use service level table or Z-table to find value of Z at 0.8

Value of Z = 0.84

Given,

Mean demand (d) = 5 million

Standard deviation (s) = 1 million

Optimal demand = d + (Z × s)

Optimal demand = 5 + (0.84 × 1)

Optimal demand = 5.84 million

Therefore, 5.84 million hardcovers should be produced.