Question $1$: $[10$ marks$]$

Lingnan Bakery $($LB$)$ uses at a steady rate of $100$ kilograms of butter to produce bread every day. The cost to order butter

from a supplier is $$50$ per order and the annual holding costs of the butter is $$H$ per kilogram. Consider LB operates $360$

days per year.

a$.$ If LB orders $500$ kilograms of butter each time and spends $$5000$ on ordering and holding the butter annually, show that

the annual holding costs of the butter per kilogram $H$ is $$5\mathrm{.}6$ per kilogram per year.

$[2$ marks$]$

b$.$ Will you advise LB to adopt the EOQ to order the butter? Justify your answer.

$[8$ marks$]$

Question $2$: $[15$ marks$]$

Reconsider question $1$:

Suppose LB can get the butter from a supplier with the following price scheme, determine the optimal order quantity in

kilograms of butter and the optimal annual total cost.