3. Toyota Co. works at its Japan plant for 300 days a year assembling 15,000 units per month. A GPS will be installed in each of the vehicles to be sold. The costs of transporting, receiving and inspecting an order are US $ 80 and the cost of keeping a piece of equipment in the warehouse is based on an annual capital cost equal to 30%. The supplier's production capacity is 45,000 units per month, which is delivered continuously during the manufacture of each batch requested, finally the supplier has a 5-day lead time cycle. Answer the following questions about the inventory policy under the supplier's sourcing policy as follows:

Lot Size ...................Unit Cost

0 ≤ Q <500   ..................$ 200

500 ≤ Q <1000 ..............$ 185

1000 ≤ Q <2500 ...........$ 170

2500 ≤ Q    ....................$ 150

a. Determine the optimal inventory management policy (lot size, cycle time, and reorder point) and its total annual cost if we assume that the sourcing policy is total discounts.

b. Determine the optimal inventory management policy (lot size, cycle time, and reorder point) and its total annual cost if we assume that the sourcing policy is incremental discounts.