The manager of a regional warehouse must decide on the number of loading docks to request for a new facility in order to minimize the sum of dock costs and driver$-$truck costs. The manager has learned that each driver$-$truck combination represents a cost of $$201$ per day and that each dock plus loading crew represents a cost of $$1,158$ per day. Use Table $18\mathrm{.}4.$

a$.$ How many docks should be requested if trucks arrive at the rate of four per day, each dock can handle five trucks per day, and both rates are Poisson?

b$.$ An employee has proposed adding new equipment that would speed up the loading rate to $5\mathrm{.}71$ trucks per day. The equipment would cost an additional $$100$ per day for each dock. What is the lowest daily total cost that can be achieved with the new equipment? $($Round your cost amount to $2$ decimal places and all other calculations to $3$ decimal places.$)$