Harry\'s Comic Book Store is trying to decide on how many copies of a book to pu

Question

Harry's Comic 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 $30.00. The publisher sells the comic book to Harry at $22.00. Harry will dispost of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Harry estimates that demand for this book during the season is Normal with a mean of 1200 and a standard deviation of 450. The publisher is thinking of offering the following scheme to Harry. At the end of the season, they will buy back unsold copies at a pre-determined price of $18.00. However, Harry would have to bear the costs of shipping unsold copies back to the publisher at $1.50 per copy. What is the quantity that Harry should order, to maximize his expected profits?

Explanation / Answer

This is a newspaper boy problem,

The Newspaper boy Model = c1/(c1+c2)

Where C1 is the cost of Unsold and C2 is the cost of purcahse.

If the vendor Giving an Option to take of unsold copy = @ $18

Cost of shipping = $1.50

Now we are calculating , the cost of unsold C1= if it is not sold we loose a profit ($30-$22) = $8 &

a loss on product value , purchasing at $22, they are taking back it at $18 = lose of $4 &

Transportation cost of $1.50

So, Total Cost of Unsold = $8+$4+$1.5= $13.50

Cost of purchasing C2= $22

Now applying Newspaper Model C1/(C1+C2)

= 13.50/(13.5+22) = 13.5/(35.5) = 0.3802

The probability = 0.3802, Means Z= -1.18

Z is the Standard Normal

It is given that the demand follows Normal Distribution With Mean 1200 and Standard Deviation is 450

Z= (X-Mean)/SD

-1.18 = (X-1200)/450

-1.18*450+1200 = X

X= 669

The optimum Quantity to Purchase in order to Maximise Profit = 669 Units.

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