Trucks arrive at a warehouse according to a Poisson process with a mean rate of $4$

per hour. Only one truck can be loaded at time. The time required to load a truck

has an exponential distribution with a mean of $10/$n minutes, where n is the number

of loaders $($n $=1,2,3,...).$ The cost are $(1)$ $$18$ per hour for each loader and $(2)$ $$20$

per hour for each truck being loaded or waiting in line to be loaded. Determine the

number of loaders that minimizes the expected hourly cost.