This is a management question:

An assembly plant purchases 35,000 air filters per year from a vendor in China that can produce them at the rate of 100,000 per year. Assembly plant's fixed ordering cost is $100 per order and it uses an inventory carrying fraction of 0.40 per year. The vendor has offered the following price schedule. For orders of more than 5,000 units, unit cost is $2.50. For orders between 1,000 and 5,000 units, filters cost $2.65. Orders less than 1,000 have a cost of $2.85 per filter.

1. Find the optimal carrying cost.

2. What is the length of the Production Period for the optimal policy?

3. Find the optimal order quantity and the optimal annual inventory, carrying, and purchasing costs for the air filters, but assume that it is an incremental-discounting pricing for the cost of filters

Please provide numerical answers.