The demand for a supply is $10,000$ items per year. The fixed cost of ordering is $$100$ per order, and holding cost is $25\%$ of product cost. The manufacturer offers a price discount according to the following table. What is the optimal lot size for this supply?

Order quantity Unit price

$<50020$

$500-99919\mathrm{.}9$

$1000-199919\mathrm{.}8$

$>=200019\mathrm{.}7$