Problem $2(50$ pts$)$

Four different part types, A$,$ B$,$ C$,$ and D$,$ have nominal dimensions $100,60,75,$ and $50,$ respectively. The table below shows three measurements for each sample. Each sample has one unit of part. If we set up the short$-$run $\stackrel{}{x}$ and $R$ charts, what are the UCL and LCL for the $\stackrel{}{x}$ chart? What are the UCL and LCL for the $R$ chart?

$\backslash$table$[[$Sample$,$Part,Measurements,Deviation from Nominal,Sample Average,Range$],[$M$1,$M$2,$M$3,x_1,x_2,x_3$