Problem $6$:

The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item are $D=600$ units, $S=$ $$\frac{20}{?}$ order and $I=30\%$ of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?

$\backslash$table$[[$Quantity$,1$ to $49,50$ to $249,250$ and up$],[$Price$,$$$5\mathrm{.}00$ per unit $$4\mathrm{.}50$ per unit $$4\mathrm{.}10$ per unit,,$]]$