USING EXCEL. 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$)$ Using the EOQ model, determine how many engines Harley should load onto each truck? $($ What is the cycle inventory of engines at Harley? What is the annual ordering cost, annual holding cost, and annual total inventory cost?

b$)$ As part of its initiative to implement just$-$in$-$time $($Jit$)$ manufacturing at the plant, Harley has reduced the number of engines loaded on each truck to $100.$ If each truck trip still costs $$1000,$ how does this decision impact annual total inventory costs at Harley? What should the cost of each truck be if a load of $100$ engines is to be optimal for Harley?