Seattle Chemicals is setting up mobile store for one week at a small city fair in a remote area of Washington State, and it is deciding on the quantity of chemical products to stock up for this event. One particular chemical product, code IB-335, is obtained from manufacturer at $100 per bottle and Seattle Chemicals sells it for $450 per bottle to its customers at the event. There is no salvage value for any leftover units of IB-335. Also, because IB-335 has short shelf life and is highly toxic, each unsold bottle must be properly disposed after the fair ends. The disposal cost is estimated to be $55 per bottle.

From the historical transaction of IB-335, it is observed that customers always buy a bottle of cleaning solution (code SC-9) together with IB-335. Therefore, it is conceivable that when IB-335 is not available, the store will also lose potential profit on SC-9. The profit margin for SC-9 is estimated at $50 per bottle.

For simplicity, you may ignore all other costs and assume that SC-9 is always available. Finally, assume that demand for IB-335 at the event is equally likely to be between 12 and 21 bottles.

What is the optimal stocking quantity for IB-335?