Problem
Montanso is a large bio firm that sells genetically modified seed to farmers at a price of $45 per kilogram (kg). Demand for the modified seed is Normally distributed with mean 450 units a month and a standard deviation of 50 units a month. The cost to produce the seed (including the cost to purchase the raw seed from the supplier) is $8 per kg. Lead time from the supplier for raw seeds is Normally distributed with mean 2 months and a standard deviation of .33 months. They store the seed in a warehouse and while the holding cost is negligible, the seed does occupy space that could be used to store another type of seed that Montanso knows it can sell at $4 a kg.
Suppose they want to maximize profit. What should their reorder level be?