$.[20$ points$]$ A Manufacturing Company makes flashing lights for toys. The company operates its

production facility $300$ days per year. It has orders for about $12,000$ flashing lights per year and

has the capability of producing $100$ per day. Setting up the light production costs $$50$ and the

holding cost is $$0\mathrm{.}10$ per light per year.

a$.$ What is the optimal production quantity during the production run?

b$.$ What is the total inventory cost per year?

c$.$ What is the length of production run in days?

d$.$ What is the maximum inventory level?