Scent of Uncertainty

You are the owner of a retail outlet that sells luxury perfume. Your challenge is to plan the inventory optimally for the upcoming year considering demand uncertainty and costs. You can only order at the beginning of the year. Unsold perfumes become obsolete after one year but can be returned to the manufacturer at a loss. You want to decide how much inventory to order to maximize expected profit.

Determine the optimal order quantity for the perfume inventory that maximizes expected profit given the discrete demand distribution and cost parameters.