$1.$ Harley$-$Davidson has its engine assembly plant in Milwaukee and its motorcycle assembly plant in Pennsylvania. Engines are transported between the two plants using trucks, with each trip costing $$1,000.$ The motorcycle plant assembles and sells $300$ motorcycles each day. Each engine costs $$500,$ and Harley incurs a holding cost of $20$ percent per year. How many engines should Harley load onto each truck? What is the cycle inventory of engines at Harley?