Production order quantity model. Please show the steps. $($Please keep $2$ decimals in your answer$)$

ABC manufacturing company makes flashing lights. The company operates its production facility $300$ days a year. It has orders for about $12,000$ flashing lights per year and has capability of producing $100$ per day. Setting up the light production costs $$50.$ The cost of each light is $$1.$ The holding cost is $$0\mathrm{.}5$ per light per year.

$($a$)$ What is the optimal size of piloduction run? $(5$ pts$)$

$($b$)$ What is the average holding cost per year? $(2$ pts$)$

$($c$)$ What is the total cost per year, including the cost of the lights? $(3$ pts$)$