Respuesta :
Answer:
It is better to order 4 copies of the magazines.
Step-by-step 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:
[tex]E[R_{3}(X)]=\sum R_{3}(X)\times P (X)\\=(-2\times \frac{1}{14})+(2\times \frac{1}{14})+(6\times \frac{3}{14})+(6\times \frac{4}{14})+(6\times \frac{2}{14})+(6\times \frac{3}{14})\\=5.143[/tex]
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:
[tex]E[R_{4}(X)]=\sum R_{4}(X)\times P (X)\\=(-4\times \frac{1}{14})+(0\times \frac{1}{14})+(4\times \frac{3}{14})+(8\times \frac{4}{14})+(8\times \frac{2}{14})+(8\times \frac{3}{14})\\=5.71[/tex]
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.
