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#$1.$ Annual demand is $74000$ per year. Holding cost, $h,$ is $$1,89$ per unit per year, and ordering cost, $S,$ is $$175$ per order. Manager, using continuous review inventory model, currently orders $5000$ units every time she$/$he places an order.

$($a$)$ How many times she$/$he places orders annually? What is the annual holding cost $HC,$ the annual ordering cost $SC$ and the total cost TC$?$

$($b$)$ What is the optimal order quantity to minimize TC$?$ What is TC$?$