Question

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.)x 1 2 3 4 5 6p(x) 1/14 1/14 3/14 4/14 2/14 3/14

Answer 1

It is better to order 4 copies of the magazines.

Explanation:

Let us assume R (X) = net revenue = Sale - Cost.

Here X is the demand of the magazines.

Then R₃ (X) and R₄ (X) represents the net revenue for 3 and 4 copies ordered respectively.

(1)

Consider that three copies of the magazines are ordered.

Total cost is, $2 × 3 = $6

The function of R₃ (X) is:

If X = 1, the revenue is, $4 × 1 - $6 = -$2

If X = 2, the revenue is, $4 × 2 - $6 = $2

If X = 3, the revenue is, $4 × 3 - $6 = $6

If X = 4, 5, 6, the revenue is $6 as the number of copies ordered is 3.

Compute the expected value of the net revenue for ordering 3 copies as follows:

`E[R_(3)(X)]=\sum R_(3)(X)* P (X)\\=(-2* (1)/(14))+(2* (1)/(14))+(6* (3)/(14))+(6* (4)/(14))+(6* (2)/(14))+(6* (3)/(14))\\=5.143`

Hence, the net revenue for ordering 3 copies is $5.14.

(2)

Consider that four copies of the magazines are ordered.

Total cost is, $2 × 4 = $8

The function of R₄ (X) is:

If X = 1, the revenue is, $4 × 1 - $8 = -$4

If X = 2, the revenue is, $4 × 2 - $8 = $0

If X = 3, the revenue is, $4 × 3 - $8 = $4

If X = 4, the revenue is, $4 × 4 - $8 = $8

If X = 5, 6, the revenue is $8 as the number of copies ordered is 4.

Compute the expected value of the net revenue for ordering 4 copies as follows:

`E[R_(4)(X)]=\sum R_(4)(X)* P (X)\\=(-4* (1)/(14))+(0* (1)/(14))+(4* (3)/(14))+(8* (4)/(14))+(8* (2)/(14))+(8* (3)/(14))\\=5.71`

Thus, the expected value of the net revenue for ordering 4 copies is $5.71.

The expected revenue for ordering 4 copies is more than for ordering 3 copies, i.e. E (R₃ (X)) > E (R₄ (X)), it is better to order 4 copies of the magazines.