Nara is a fashion apparel and accessories chain store that procures a line of new shorts at $10 each from its European supplier. Unfortunately, at the time of order placement, demand is still unknown.
Nara forecasts that its demand is normally distributed with mean of 2100 and a standard deviation of 1200 units. Nara sells these shorts at $22 each. Unsold shorts have little salvage values and they would be donated to charity.
Based on this information:
How many shorts should Nara buy from its supplier to maximize expected profit?
If Nara wants to ensure a 98.5% in-stock probability, how many shorts should it order?
Suppose Nara decided that the donations of unsold shorts actually had a positive material effect on the company in the form of public goodwill.
If this goodwill is estimated to be about $3 per donated item, how many shorts should Nara buy from its supplier to maximize expected profit?