Arthur meiners is tge production manager of wheel rite, a small producer of metal parts. Wheel rite supplies cal$-$tex, a larger assembly company with $10000$ wheel bearing each year. This order has boon stable for some tome. The set up cost for wheel rite is $50$ and holdind cost is $50$ per wheel bearing per year. Wheel rite can produce $500$ wheel bearing per day. Cal tex is a just in time manufacturer abd requires that $50$ bearings be shipped to it each business day.

$1)$ what is optimum production quantity $?$