A manufacturer $($called $$manufacturer A$)$ is reviewing its stocking and replenishment policy

for a commodity component used for the production of lawn mowers. A single unit of the

component is used for each lawn mower, and the average production rate is of $30$ lawn

mowers per day. $($The manufacturing plant is open $365$ days per year.$)$ Components are

shipped to the manufacturer in a truck, and each time an order is placed it costs the

manufacturer $$240$ to place the order $($as long as the quantity purchased is lower than the

truck$$s capacity of $600$ units$).$ It costs about $$20$ to hold a unit of a component in stock for

one year.

a$.$ Calculate the EOQ that the manufacturer should use for ordering components. $($Round up

to the nearest integer.$)$

b$.$ How often will the manufacturer receive an order? $($Round to the nearest integer.$)$

c$.[$Note: Less$-$than$-$truckload shipment refers to the case where the shipment quantity is less

than the capacity of a standardized truck.$]$

Because of the manufacturer$$s current ordering needs, components are delivered in LTL

$($less$-$than$-$truckload$)$ shipments. Manufacturer A is contemplating initiating a pool

distribution agreement with another manufacturer $($called $$manufacturer B$)$ located in the

same industrial park. In other words, these manufacturers agree to order and manage

inventory together to meet their combined demand. Manufacturer B buys components from

the same supplier and its plant is also open $365$ days per year. However, manufacturer B

uses these components at an average rate of $10$ components per day. It incurs the same

holding cost as manufacturer A and because it places orders with the same supplier, it also

incurs $$240$ to place an order.

What is the EOQ for the pool distribution agreement? If they split the fixed ordering cost

and the quantity received in each shipment in proportion to their demands, how much will

manufacturer A save on average in inventory and ordering costs?