Sweet Treats sells its extra- large cupcakes for $12 each and the firm has a constant marginal cost of $8 per cupcake, which is equal to its (constant)average total cost. If Sweet Treats does not sell a cupcake the day it is produced, it is sold as day- old for $4. Sweet Treats should hold the number of cupcakes in inventory that makes the probability of selling that quantity of cupcakes or more equal to_______ .

Question

Quizplus · Accepted Answer

To find the optimal inventory level, we need to determine the probability that a given quantity of cupcakes will sell. Let's assume that demand follows a normal distribution with a mean of 25 cupcakes and a standard deviation of 5 cupcakes (based on historical sales data).

The probability of selling a certain quantity of cupcakes or more is equal to the probability that demand exceeds that quantity. Using a standard normal distribution table, we can find that the probability of demand exceeding 20 cupcakes is approximately 0.50. Therefore, Sweet Treats should hold an inventory level of 20 cupcakes, which makes the probability of selling that quantity or more equal to 0.50.

If the firm holds fewer cupcakes, the probability of stockouts and lost sales increases. If the firm holds more cupcakes, the probability of excess inventory and markdowns increases, which would reduce the firm's profitability. Therefore, the optimal inventory level is 20 cupcakes.

Sweet Treats Sells Its Extra- Large Cupcakes for $12 Each