An aircraft wing manufacturer based in Montreal currently purchases aluminum parts for its wings overseas in England. It has traditionally used a combination of ocean liner and truck to deliver these parts from England. As Director of Operations Management at the aircraft wing manufacturer, you would like to assess other modes of transport to ensure the current mode is lowest cost. Annual demand is 5000 parts.

Using an ocean liner to cross the Atlantic Ocean costs $50 per part and will take 9 days. Then the truck from the port of Montreal to the wing plant in Montreal costs $20 per part and takes 3 days. This is the current mode of transport.

As an alternative, parts can be flown directly to Montreal at a cost of $115 per part, including delivery charges at destination. Delivery is 2 days.

A third alternative is to use the ocean liner at $50 per part and 9 days delivery, and then train from the port of Montreal. Transport by train will cost $25 and will take 5 days.

The companys inventory holding cost rate is 12% per year and the price of each part is $8000.

Due to the variability of lead times, quantities of safety stocks of 100 units for ship and truck, 150 units for ship and train and 30 units for air will be kept for each respective mode of transport.

Determine the lowest cost mode of transport for these aluminum parts

( Please show all your steps and calculations process)