Let's consider the inventory problem with quantity discounts. The parameters are as follows:

Annual demand lambda $=25000,$

Order cost K $=100,$

I $=0\mathrm{.}3.$

For order quantities between $0$ and $499,$ you pay c$($Q$)=21\mathrm{.}60$ per unit

For order quantities between $500$ and $999,$ you pay c$($Q$)=20\mathrm{.}95$ per unit

For order quantities $>=1000,$ you pay c$($Q$)=20\mathrm{.}90$ per unit.

What is your total cost per year if your order quantity is $680$ per order?

What is the optimal order quantity $($round your final answer to the nearest integer$)?$