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.

a$.$ How many engines should Harley load onto each truck?

b$.$ As part of its initiative to implement just in time $($JIT$)$ manufacturing at the motorcycle assembly plant, Harley has reduced the number of engines loaded on each truck to $100.$ If each truck trip still costs $$1,000,$ how does this decision impact annual inventory costs at Harley?