A part is processed in the following sequence: Machine $B>>$ Machine $A>>$ Machine $C.$ Machines $A,B,$ and $C$ are known to have scrap rates of about $2\%,3\%,$ and $4\%.$

$($a$)$ If $1000$ units of the part must be produced each day, approximately how many parts must be processed by Machine A each day? Show work. $(15$ points$)$

$($b$)$ The company's Quality Control department is projecting that given the age of the machines, each of the machines $A,B,$ and $C$ will have a scrap rate next year that will be $1\%$ higher. By what percentage will the number of parts processed by Machine A each day go up next year? Show work. $(10$ points$)$