ack is managing the vaccine for coronavirus for a clinic. Since the demand is always at capacity it is constant. The capacity is $3000$ patients per month. Each patient needs one dose.

Every time Jack place an order, he needs to pay a fixed ordering cost of $$500.$ Since the vaccine needs refrigeration, it cost $$1$ per dose per month to hold. The unit cost per dose is $$100.$ The interest rate is close to zero, therefore, the capital cost is negligible.

Jack wants to determine how many doses to order to minimize the total inventory cost.