Assignment task: Michelle Abrams runs a specialty clothing store that sells collegiate sports apparel. One of her primary business opportunities involves selling custom screen printed sweatshirts for college football bowl games. She is trying to determine how many sweatshirts to produce for the upcoming Tangerine Bowl game. During the month before the game, Michelle plans to sell sweatshirts for $30 each. At this price, she believes the demand for sweatshirts will be normally distributed with mean 7,000 and standard deviation 1,500 (with no negative values). During the month after the game, Michelle plans to sell any remaining sweatshirts for $12 each. At this price, she believes the demand for sweatshirts will be discrete uniformly distributed with a minimum demand of 300, and a maximum demand of 1,000. Two months after the game, Michelle plans to sell any remaining sweatshirts to a surplus store that has agreed to buy up to 1,500 sweatshirts for a price of $3 per shirt. Michelle can order custom screen printed sweatshirts for $10 per sweatshirt in lot sizes of 1000.
1. Develop a descriptive model of this scenario; identify and name random and non-random variables along the way. You may develop a flowchart for yourself to help you visualize, but do not attach it to the submission.
2. List all random variables, their distributions, and parameters.
3. Code the model in Excel and replicate it 10,000 times. Answer the following questions (do not attach the spreadsheet):
- Determine the average profit that Michelle would earn if she orders 10,000 sweatshirts.
- Find the probability that Michelle's profit would be less than or equal to $100,000 if she orders 10,000 sweatshirts.
- How many sweatshirts would you recommend Michelle order to maximize average profit?