Reed Juices Limited purchases $25,000$ litres of a material each year from a single supplier. At the

moment, the company obtains the material in batch sizes of $800$ litres. The material costs $$16$ per

litre, the cost of ordering a new batch from the supplier is $$32$ and the cost of holding one litre in

stock, due to certain technical difficulties, is $$4$ per annum plus an interest cost equal to $15\%$ of the

purchase price of the material.

The supplier has agreed to offer a discount on orders above a certain size. He has

offered the following price structure:

Order size $($litres$)$ Unit cost $($$$)$

$0-49916\mathrm{.}00$

$500-99915\mathrm{.}20$

$1,000$ plus $14\mathrm{.}80$

Required:

$($a$)$ Prior to considering discounts: calculate the economic order quantity and the annual savings

that will be obtained if the EOQ replaced the current lot size.

$($b$)$ The supplier has offered quantity discounts based on the price structure indicated above,

after considering discounts, how does this affect the optimal order quantity, and what would

be the annual savings compared to the inventory costs with the EOQ you calculated in $($a$)?$

$($c$)$ At a recent meeting, Michael Wong, one of Reed$$s Ltd senior managers stated that the

company should not use the EOQ model because it is based on unrealistic assumptions and

no one in the company really understands how the model works. Draft a memo addressed to

the company$$s managing director to respond to Mr$.$ Wong$$s concerns.