Pratt & Whitney, a major aircraft engine manufacturer, wants to re$-$evaluate the transportation mode it uses to send unfinished parts to its joint$-$venture facility in Chengdu, China. Annual demand is $2,600$ units. At present the company uses air freight. It takes approximately six days from Los Angeles to Chengdu $($including pickup and delivery and customs delays$).$ There are $30$ parts in a lot, each weighing $35$ kilograms. The air freight cost per part is $$90.$ The pickup and delivery charges at origin and destination add up to $$14$ per part. The alternative is to use an ocean liner to ship the parts to Shanghai and from there to either use a truck or a train $($a $2,000$ km distance$).$ The ocean freight for this lot size will cost $$25$ per part and will take $15$ days. The truck from Shanghai to Chengdu will cost $$22$ per part and will take six days $($including pickup and delivery and customs delays$).$ Transportation by rail will cost $$18$ per part and will take $14$ days $($including pickup and delivery, customs, and transfer delays$).$ In addition, for rail there is a $$11$ per part charge for pickup and delivery. The company$$s inventory holding cost rate is $12$ percent per year, and the value of each part is $$900.$ Assume $365$ days per year.

Due to variability of lead times, at the destination, safety stocks of $80,240,$ and $320$ units will be kept if air, ship and truck, and ship and train are used, respectively. Determine the cheapest $($total freight, delivery, and in$-$transit and safety holding cost$)$ mode of transportation for these parts. Hint: The value of a part in Chengdu for calculating the safety$-$stock holding cost should include the freight cost.