Question $6(8$ points$)$ A machine needs to be purchased to cut metal bars into pieces of varying target lengths. The typical specification calls for cutting pieces with a tolerance of $4$mm$,$ e$.$g$.$ if the target length is $500$mm$,$ then all cut pieces with length between $496$mm and $504$mm are acceptable. Three machines, A$,$ B$,$ and C$,$ are being considered. All are able to achieve average length equal to any given target length $($i$.$e$.$ average length will be centered between specification limits$).$ Machine A costs $$1,000$ and can cut parts with a standard deviation of $1\mathrm{.}5$mm$.$ Machine B costs $$1,200$ and has standard deviation of Imm. Machine C costs $$2,000$ and has standard deviation of $0\mathrm{.}4$mm$.1.$ Which machine would you recommend? Justify your answer briefly. $(6$ points$)2.$ Which machine would you recommend if a company were interested in implementing a Six Sigma program? Justify your answer briefly, $(2$ points$)$