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

Lingnan Bakery $($LB$)$ uses at a steady rate of $50$ kilograms of wheat flour to produce bread daily. The cost to order wheat flour from a supplier is $$S$ per order and the annual holding costs of the wheat flour is $$10$ per kilogram. Consider LB operates $300$ days per year.

a$.$ If LB orders $1000$ kilograms of wheat flour each time and spends $$12500$ on ordering and holding the wheat flour annually, show that the ordering cost of the wheat flour per order $S$ is $$500$ per order

$[2$ marks$]$

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

$[8$ marks$]$

Question $2$: $[16$ marks$]$

Reconsider question $1.$

Suppose the parameters of question $1$ remain and LB can get the wheat flour from a supplier with the following price scheme, determine the optimal order quantity in kilograms of wheat flour and the annual total cost.

$\backslash$table$[[$Weight in Kilograms,Unit Price per kilogram$],[1$ to $749,$$$8\mathrm{.}0][750$ to $1499,$ $$7\mathrm{.}5][1500$ or more, $$6\mathrm{.}5]$