Prefab$2,$ ?a furniture manufacturer, uses $2,000$ ?square feet of plywood per month. Its trucking company charges Prefab$2$ ?$$400$ ?per shipment, independent of the quantity purchased. The supplier offers an all unit quantity discount with a price of $$1$ ?per square feet for all orders under $6,000$ ?square feet, $$0\mathrm{.}98$ ?per square feet for all orders of $6,000$ ?or more square feet but under $12,000$ ?square feet, and $$0\mathrm{.}96$ ?per square feet for all orders of $12,000$ ?or more square feet. Prefab$2$ ?incurs a holding cost of $25$ ?percent. What is the optimal lot size for Prefab$2?$

Group of answer choices

$8,853$

$8,944$

$12,000$

$10,000$