Connecticut Computer Corporation $($CCC$)$ is a Connecticut$-$based retailer of an electronic device called Digital Diagnostics Device $($DDD$),$ which CCC sources from a supplier. CCC has four retail outlets in Connecticut. Currently each outlet manages its ordering of DDD independently, placing orders directly with the supplier. The rate of demand for DDD at each outlet is constant at $200$ units per week. There is no uncertainty in the demands. Each unit of DDD costs $$200$ to purchase and its annual inventory holding cost percentage is $20\%.$ The fixed cost of each order $($administrative plus transportation$)$ is $$900.$ For simplicity, assume that the shipping lead time is negligible and that the supplier can promptly deliver all orders. Assume $50$ weeks in a year.

$1.$ Given that each of the four outlets orders independently and gets its own delivery, what is the optimal order quantity at each outlet?

$2.$ What is the sum of annual ordering cost and annual holding cost for all four outlets combined?