An electronics manufacturer ships partially assembled circuit

boards $($hereafter called units$)$ from an assembly plant in Jorda

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An electronics manufacturer ships partially assembled circuit boards $($hereafter called units$)$ from an assembly plant in Jordan to a distribution center in UK$.$ We want to determine which transportation mode is lower in terms of total shipping cost. There are two options for shipping, the first is to ship in $40$ft containers by ocean carriers or in airline containers by air carriers. Shipment by ocean costs $$10,000$ per container, and a $40$ft container can hold $4,500$ units. The handling cost is $$1,500$ per $40$ft container. The journey by sea takes $20$ days on average. Shipment by air costs $$20,000$ per container, and an airline container can hold $1,400$ units. The handling cost is $$800$ per airline container. The journey by air takes $2$ days on average $($door to door$).$ The forecasted demand is $120,000$ units for the next year, which is also the planned production quantity. No safety stock is kept at the assembly plant, and a shipment is sent to the distribution center as soon as a container is filled. Safety stock of $800$ units is kept at the distribution center. A unit is valued at $$500$ at the assembly plant and $$700$ at the distribution center. The inventory holding cost rate is estimated at $15\%$ of the value per year. The space cost is estimated as $$30/$unit$*$year at the assembly plant and $$40/$unit$*$year at the distribution center. Which transportation mode is more economical in terms of total annual $($transportation and inventory$)$ cost$?($Show your work for all cost elements and find the optimum shipment size$).$ In the blank below, fill in the optimal shipment size for the ocean mode $($round to the nearest integer$).$