$($b$)$ 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 $10,000$ wheel bearings each year. This order has been stable for some time. Setup cost for Wheel$-$Rite is $$40,$ and holding cost is $$\mathrm{.}60$ per wheel 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 be shipped to it each business day. $[4$ marks$]1)$ What is the optimum production quantity?II$)$ What is the maximum number of wheel bearings that will be in inventory at Wheel$-$Rite?iii$)$ How many production runs of wheel bearings will Wheel$-$Rite have in a year?Iv$)$ What is the total cost for Wheel$-$Rite?