A major consumer electronics and furniture retailer in Singapore is reviewing the inventory

management system of its portable powerbanks for charging electronic devices. Currently,

the retailer uses the fixed$-$quantity inventory system with an order quantity of $900$ units.

Based on historical data, the monthly demand is estimated at $400$ units. The ordering cost

is $$500$ per order, the unit price is $$25,$ and the carrying rate is $30\%.$

Analyse whether the order quantity of $900$ units is the optimal value to minimise total

annual cost. If yes, what is the total annual cost? If not, what is the optimal order quantity and what is the total annual cost difference between these two order quantities?Support your answer with calculations.