$6-31.$ A new manufacturing facility will produce two products, each of which requires a drilling operation during processing. Two alternative types of drilling machines $($D$1$ and D$2)$ are being considered for purchase. One of these machines must be selected. For the same annual demand, the annual production requirements $($machine hours$)$ and the annual operating expenses $($per machine$)$ are listed in Table P$6-31.$ Which machine should be selected if the MARR is $15\%$ per year? Show all your work to support your recommendation. $(6\mathrm{.}5)$

Assumptions: The facility will operate $2,000$ hours per year. Machine availability is $80\%$ for Machine D$1$ and $75\%$ for Machine D$2.$ The yield of $D1$ is $90\%,$ and the yield of $D2$ is $80\%.$ Annual operating expenses are based on an assumed operation of $2,000$ hours per year, and workers are paid during any idle time of Machine D$1$ or Machine D$2.$ State any other assumptions needed to solve the problem.