A local retailer of plumbing supplies faces demand for one of its SKUs at a constant rate of $9,000$ units per year. The unit cost of the SKU is $10$ per unit. The cost of capital is $10\%$ per year, which implies the annual holding cost per unit is $10\%$ of $10.$ It costs the retailer $20$ to process an order to replenish stock.

What is the optimal order quantity of the SKU in each order cycle?