The Warehouse Company supplies spare parts for its two plants, Plant A and PlantB. Plant A and Plant B do not have any significant storage space. Hence you want carryminimum possible inventory at the plants A, B.

The warehouse W stocks two types ofspare parts, part #A for the Plant A and part #B for the Plant B. The WarehouseCompany uses a state of the art automated retrieval system (ARS) to retrieve parts fromstorage in the warehouse.

Part # A: The retrieval system takes 1 minute/unit to retrieve and send the part to theloading dock.

Part # B: The retrieval system takes 1 minute/unit to retrieve and send the part to theloading dock.

Whenever the retrieval system has to switch from part #A to part #B, there is a "deadloss" of 30 minutes.

Whenever the retrieval system has to switch from part #B to part #A, there is a "deadloss" of 30 minutes.

The demand for A at the Plant A is deterministic and is 15 units /hr. or 360units/day.

The demand for B at the Plant B is deterministic and is 15units /hr. or 360units /day.

Assume that a Day=24hrs. Thus, Plant A, Plant B, and the Warehouse Company are all open around the clock.

Plant A and Plant B and the Warehouse Company are all located in Houston, and hencethe transportation time from the loading dock of the Warehouse Company to the plants isnegligible.

The goal is to use the ARS efficiently so as to keep the plants busy as much as possible. Design a scheme to use the ARS efficiently. Specifically,

a. How many units of part A will be retrieved and shipped before you switch to part B?

b. How many units of part B will be retrieved and shipped before you switch to part A?