Problem $18-7($Algo$)$

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 $$262$ per day and that each dock plus loading crew represents a cost of $$1,147$ 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?

Number of dock$(s)$

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 ploces and all other calculatlons to $3$ decimal places.$)$

The daily total cost with the new equipment is