The IMU bookstore needs your help to determine the number of Cachon and Terwiesc

Question

The IMU bookstore needs your help to determine the number of Cachon and Terwiesch’s book (our textbook) to purchase before the 2018 summer session opens. The book retails at $100. McGraw Hill sells the book to IMU for $75. IMU will dispose of all the unsold copies of the book at 85% off the retail price at the end of the summer session. IMU estimates that demand for this book is Poisson with mean of 9 units. As an incentive for IMU to order more of Cachon and Terwiesch’s book, McGraw Hill is offering the following deal. At the end of the summer session, McGraw Hill will buy back unsold copies of the book for $35. However, IMU would have to bear the cost of shipping unsold copies back to McGraw Hill at $2.00 per copy. Find the expected profit maximizing answers to the following questions.

Suppose IMU store orders 6 books, what is IMU’s approximate expected profit if McGraw

Hill offers the buyback incentive?

a. 137

b. 145

c. 245

d. 345

e. 445

Explanation / Answer

Profit per sold book = 100-75 =25

Loss per unsold book = 75- 35 -2 = 38

Probability of sale of x units, when the mean is m units is given by

P (x) = exp(-m) mx / x!

Probability that the demand will be less than 6 units

P (x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)

exp(-9) * 90 / 0! + exp(-9) 9/1! + exp (-9) *92 / 2! + exp (-9) * 93 / 3! + exp(-9) * 94 / 4! + exp (-9) * 95 / 5!

0.00012+ 0.00108+0.00486+0.01458+0.0328+0.06 = 0.1125

Expected profit from 6 units = 25x6 =150

Expected loss if less than 6 units sell  

0.00012 x38x6+0.00108x38x5+0.00486x38x4+0.01458x38x3+0.0328x38x2+0.06x38x1 =

0.02736+0.2052+0.738+1.66+2.49+2.28 = 7.40

Expected profit = 150-7.40 = 137.6

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