Question

Costco plans on stocking a Christmas tree for the holiday season. The product is only sold in November and December. The order lead time is longer than two months so Costco can only place one order for the Christmas tree. Based on historical sales, Costco believes that the demand for the tree during the season is normally distributed with an average of 450 units and a standard deviation of 180 units. Costco purchases the trees at $79 each and sells them at $180 each. Any unsold tree at the end of the year will be sold to a discounted store at $55 each. Costco currently purchase 525 trees.

a. What is the probability that Costco will run out of stock before end of December?

b. What is the expected number of unsold trees at the end of December?

c. What is Costco’s expected profit from selling the tree?

Answer 1

a.

Let’s assume we get the trees before the shopping season begins. This means we have 525 trees in stock. In order to not run out of stock the demand should be below 525. This means the z value will be

z = (525 – 450)/180 = 0.41667

The probability will be P(z) = 0.6591 or 65.91% probability that they will not run out of stock. This means the probability of running out of stock is 1-0.6591=0.3409 or 34.09%

b.

Expected number of unsold trees will be

525 – 450 = 75 trees.

The expected number of unsold trees is 75 trees

c.

Costco will make a profit of (180-79)*450 = 45450 from the sale of the trees

When it comes to the unsold trees, Costco will be left with 75 trees and will sell them for 55 and incur a loss of (79-55)*75 = 1800.

The total profit will be 45450 – 1800 = 43650