Question

3.3) A small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with the following pmf.

x	1	2	3	4	5	6
p(x)	1 13	1 13	3 13	4 13	2 13	2 13

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: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue.]

*What is the expected profit if three magazines are ordered? (Round your answer to two decimal places.)

*What is the expected profit if four magazines are ordered? (Round your answer to two decimal places.)

*How many magazines should the store owner order?

-3 magazines

-4 magazines

Answer 1

Let X be the quantity of demand. Let Q be the quantity that the store owner orders.

The quantity that he can sell (S) is minimum of X and Q. (He can not sell more than what he orders or more than the demand)

The cost to order Q magazines is 2Q

the revenue from selling S magazines is 4S

The profit is 4S-2Q

The expected profit is

What is the expected profit if three magazines are ordered?

the following table gives the profit for ordering 3 magazines

Demand (X)	p(x)	Order Quantity	Quantity sold	Cost to order ($)	Revenue ($)	Profit
1	1/13	3	1	6	4	-2
2	1/13	3	2	6	8	2
3	3/13	3	3	6	12	6
4	4/13	3	3	6	12	6
5	2/13	3	3	6	12	6
6	2/13	3	3	6	12	6

The expected profit from ordering 3 magazines is

What is the expected profit if four magazines are ordered?

the following table gives the profit for ordering 4 magazines

Demand (X)	p(x)	Order Quantity	Quantity sold	Cost to order ($)	Revenue ($)	Profit
1	1/13	4	1	8	4	-4
2	1/13	4	2	8	8	0
3	3/13	4	3	8	12	4
4	4/13	4	4	8	16	8
5	2/13	4	4	8	16	8
6	2/13	4	4	8	16	8

The expected profit from ordering 4 magazines is

The expected profit if 4 magazines are ordered is $5.54 and is greater than the expected profit when 3 magazines are ordered.

Hence the store owner should order 4 magazines