The Friendly Sausage Factory $($FSF$)$ can produce hot dogs at a rate of $5,000$ per day. FSF supplies hot dogs to local restaurants at a steady rate of $250$ per day. The cost to prepare the equipment for producing hot dogs is $$66.$ Annual holding costs are $45$ cents per hot dog. The factory operates $300$ days a year. Find: a$.$ the optimal run size b$.$ the number of runs per year c$.$ how many days it takes to produce the optimal run quantity