Arthur Meiners is the production manager of Wheel$-$Rite, a small producer of metal parts. Wheel$-$Rite supplies Cal$-$Tex, a larger assembly company, with $10,100$ wheel bearings each year. This order has been stable for some time. Setup cost for Wheel$-$Rite is $$42,$ and holding cost is $$0\mathrm{.}40$ per wheel bearing per year. Wheel$-$Rite can produce $460$ wheel bearings per day. Cal$-$Tex is a just$-$in$-$time manufacturer and requires that $47$ bearings be shipped to it each business day.

a$)$ What is the optimum production quantity? units $($round your response to the nearest whole number$).$