Question

A small market orders copies of a certain magazine for its magazine rack each week. Let X weekly demand for the magazine, with pmif 2. 4 Px(x 1/15|2/15 | 4/154/153/15 | 1/15 Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? Hint: Create two new random variables, call the Yi and Y2, where Yi-net revenue (income due to sold magazines - cost to purchase and stock the magazines) for the and E(Y2).

Answer 1

Income due to sold magazine = $(4-2) = $2

Cost to purchase and stock magazine = $2 .

Note that :

if x is the demand/ number of copies sold , then

FOR 3 COPY STRATEGY :

$Y_1 = 2 x - 2 \times (3-x) = 4x-6$ when x = 0,1,...3

= 6 when x = 4 , 5

and $Y_2 = 2 x - 2 \times (4-x) = 4x-8$ when x = 0,1,....4

= 8 when x = 5

So, pmf of Y₁ is :

Y1	-6	-2	2	6
P[Y1]	1/15	2/15	4/15	8/15

So,

EM = Σ yi.PMI 3.067

and pmf of Y₂ :

Y2	-8	-4	0	4	8
P[Y2]	1/15	2/15	4/15	4/15	4/15

So, $E[Y_2] = \Sigma \left y_2 .P[Y_2] = 2.13$

As E[Y1]> E[Y2] , it is suggested to go for 3 copy strategy.