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 $9,600$ wheel bearings each year. This order has been stable for some time Setup cost for Wheel$-$Rite is $$39,$ and holding cost is $$0\mathrm{.}80$ per wheel bearing per year. Wheel$-$Rite can produce $510$ 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? $1,015$ units $($round your response to the nearest whole number$).$

b$)$ What is the maximum number of wheel bearings that will be in inventory at Wheel$-$Rite? units $($round your response to the nearest whole number$).$N