How many machines should you buy and how many people should you hire if $6400$ units are needed per shift in a $80$ percent efficient plant that has $10$ percent downtime? The machine time standard is $\mathrm{.}224$ minute. How much will a unit cost to produce if the operator earns $$18$ per hour? How many units will be produced per shift? What is the takt time? $(10$ points$)$