A retailer sells three colors of t-shirts – red, green and blue. The t-shirts are procured before the start of the selling summer season and no additional procurement during the selling season is possible. Demand for each color during the summer selling season is normally distributed with mean 50 and standard deviation 20 and demands for the different colors are uncorrelated.
Each t-shirt costs $10 to buy from the manufacturer and sold to customers for $25. At the end of the summer selling season, t-shirts are sold at a discounted price of $7.50.
Suppose the retailer has a budget of $3000 for procurement. What is the retailer's expected profit?
