Answer to Question #292277 in Economics of Enterprise for george2000

Question

The daily demand for a product in a shop can assume one of the following values: 100, 200, or 300 items with probabilities 0.2, 0.5 and 0.3. The owner of the store is thus limiting the alternatives to stocking one of the indicated three levels. If the owner stocks more that it can be sold in the same day the remaining items must be disposed at a discount price of 50 cents per item. Assume that the owner pays 80 cents per item and sells it for 120 cents, find the optimal stock level.

Answer 1

To find the optimum level of stock, with the data given we find initial stock in each and its net fetch from the sale and disposal of the extra unsold by the end of the day.

In the probability of having demand of 100, total stock is expected to have been;

$\frac{1}{0.2}\times100=500$

the net revenue obtained from having a stock of 500 is;

$-500(80)+120(100)+50(400)=-8000$

Probability of a 200 unit demand, total expected stock is;

$\frac{1}{0.5}\times200=400$

net revenue from the stock of 400 is;

$-400(80)+120(200)+50(200)=2000$

with a demand of 300 units total expected stock is;

$\frac{1}{0.3}\times300=1000$

net expected revenue from 1000 stock level is;

$-1000(80)+120(300)+50(700)=-9000$

From the obtained net revenues, a stock level of 400 managed a profit 2000. 400 stock level therefore is the optimal level of stock the shopkeeper should maintain.