$2.($Inventory Management $-$ Part $1)$ A manager just received a new price list from supplier. It will now cost $\backslash (\backslash$$ $1\mathrm{.}00\backslash )$ a box for order quantities of $801$ or more boxes, $\backslash (\backslash$$ $1\mathrm{.}1\backslash )$ a box for $200$ to $800$ boxes, and $\backslash (\backslash$$ $1\mathrm{.}20\backslash )$ for smaller quantities. Ordering cost is $\backslash (\backslash$$ $80\backslash )$ per order and carrying costs are $\backslash (\backslash$$ $10\backslash )$ per box a year. The firm uses $3,600$ boxes a year. The manager suggested a "round number" order size of $800$ boxes. The manager's rationale is that with a U$-$shaped cost curve that is flat at its minimum, the difference in total annual cost between $800$ and $801$ units would be small anyway. How would you reply to the manager's suggestion? What order size would you suggest?