Question $4(3$ points$)$

$6-20($c$).$ Lila Battle has determined that the annual demand for number $6$ screws is $100,000$ screws. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $$10$ every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on$.$ Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one$-$half of $1$ cent. Assume that the demand is constant throughout the year.

c$.$ The average inventory would be $x$ units with an annual holding cost of $y.$ Select the best answer from the choices below.

$10,000$ for $x$

$$50$ for $y$

$9,000$ for $x$

$$45$ for $y$

$10,200$ for $x$

$$53$ for $y$

$9,800$ for $x$

$$51$ for $y$