Question

T-shirts cost $4 to make/distribute and sell for $10. Company policy is to dispose of any excess inventory after the event by discounting the T-shirts by 95 percent, that is, sell them for $0.50. Traditionally, all discounted shirts can be rapidly sold at this price.

T-shirt demand at the Chillicothe Marathon is normally distributed with mean 120 and standard deviation 40. How many T-shirts should Champion Apparel print to maximize expected profit?

Answer 1

To maximize expected profit, Champion Apparel should determine the optimal quantity of t-shirts to print based on the demand distribution and the desired profit level.

Step-by-step explanation:

To maximize expected profit, Champion Apparel should print the number of t-shirts that corresponds to the highest expected demand. In this case, the demand follows a normal distribution with a mean of 120 and a standard deviation of 40. To find the optimal quantity, we can use a statistical concept known as the Z-score. The Z-score measures how many standard deviations a particular value is from the mean. Using the Z-score formula, we can calculate the Z-score for the desired profit level, which in this case is $10 - $4 = $6. Next, we can convert the Z-score to a probability using a standard normal distribution table. Finally, we can multiply this probability by the total possible demand to determine the optimal quantity of t-shirts Champion Apparel should print.