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 $10000$ wheel bearings per year, This order has been stable for some time. The set up cost for wheel rite is $$50$ and holding cost $$50$ per bearing per year. Wheel rite can produce $500$ wheel bearings per day. Cal$-$Tex is a just in time manufacturer and requires that $50$ bearings can be shipped to each business day.

$1)$ What is optimum production quantity

$2)$ What is the maximum number of wheel bearings that will be in inventory at wheel rite

$3)$ How many production runs of wheel bearings will wheel rite have in a year!

$4)$What is total cost of Wheel rite?