ABS factory sells filters at a steady rate of $15000$ per year. ABS estimates that the cost of setup per production run is equal to $$500.$ Holding cost of each filter is $$50$ per year. Capacity of production for ABS factory is $25000$ units per year. Factory works $240$ days per year.

a$)$ What should be the amount of the production for each run to minimize the costs?

b$)$ What is the maximum inventory level

c$)$ What is the total number of production runs per year.

d$)$ What is the length of each production run?

e$)$ What is the time between productions?