a$.$ Optimal Order Quantity $($EOQ$)$:

EOQ$=((2\backslash$times D$\backslash$times SH$)/$H$)$

where:

D $=$ Demand per day $=20$ units$/$day

S $=$ Ordering cost $=$ $$50$

H $=$ Holding $($carrying$)$ cost per unit per year $=20\%$ of the unit cost

First, need to calculate the unit cost:

For orders of $1,000$ or less, the unit cost $=$$$5\mathrm{.}00$

For orders of $1,000$ or more, the unit

cost $$4\mathrm{.}75$

Let's calculate the EOQ:

Unit cost $=$ $$5\mathrm{.}00($EOQ will be based on the lower unit cost$)$

H $=20\%$ of $$5\mathrm{.}00=$ $$1\mathrm{.}00($Holding cost per unit per year$)$