Exercise $8$: Demand for a certain product is $25,000$ units$/$year$.$ Holding cost per piece is $$3.$ Change$-$over $($set$-$up$)$ time between products is $10$ hours, and downtime cost during change$-$over is $$\frac{150}{?}$ hour.

a$)$ Determine the EOQ,

b$)$ Calculate the ordering, holding, and total inventory costs,

c$)$ How many orders will be placed each year?

d$)$ How much time will elapse between the placements of orders? Assume $360$ days per year.