Montanso is a large bio firm that sells genetically modified seed to farmers. They need to decide how much seed to put into a warehouse to serve the demand for the next growing season. They will make one quantity decision. It costs Montanso $$8$ to make each kilogram $($kg$)$ of seed. They sell each kg for $$45.$ If they have more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, they only earn $$3$ per kg from the overseas market $($but this is better than destroying the seed because it cannot be stored until next year$).$ If demand exceeds their quantity, then the sales are lost, and the farmers go to another supplier. As a forecast for demand they will use a normal distribution with a mean of $150,000$ and a standard deviation of $110,000.$

How many kilograms should they place in warehouse if they want to minimize inventory while ensuring stockout probability is no greater than $10\%$