Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility $300$ days per year. It has orders for about $11,600$ flashing lights per year and has the capability of producing $95$ per day. Setting up the light production costs $$49.$ The cost of each light is $$0\mathrm{.}95.$ The holding cost is $$0\mathrm{.}05$ per light per year.

a$)$ What is the optimal size of the production run? $6192$ units $($round your response to the nearest whole number$).$

b$)$ What is the average holding cost per year? $$91\mathrm{.}79($round your response to two decimal places$).$

c$)$ What is the average setup cost per year? $$91\mathrm{.}80($round your response to two decimal places$).$

d$)$ What is the total cost per year, including the cost of the lights? $ $($round your response to two decimal places$).$