A part is produced using six conventional machine tools consisting of three milling machines and three drill presses. The machine cycle times on these machines are $4\mathrm{.}7$ min, $2\mathrm{.}3$ min, $0\mathrm{.}8$ min, $0\mathrm{.}9$ min, $3\mathrm{.}4$ min, and $0\mathrm{.}5$ min. The average load$/$unload time for each operation is $1\mathrm{.}25$ min. The corresponding setup times for the six machines are $1\mathrm{.}55$ hr$,2\mathrm{.}82$ hr$,57$ min, $45$ min, $3\mathrm{.}15$ hr$,$ and $36$ min, respectively. The total material handling time to carry one part between the machines is $20$ min $($consisting of five moves between six machines$).$ A computer numerical control machining center has been installed, and all six operations will be performed on it to produce the part. The setup time for the machining center for this job is $1\mathrm{.}0$ hr$.$ In addition, the machine must be programmed for this part $($called $$part programming$),$ which takes $3\mathrm{.}0$ hr$.$ The machine cycle time is the sum of the machine cycle times for the six machines. Load$/$ unload time is $1\mathrm{.}25$ min. $($a$)$ What is the total time to produce one of these parts using the six conventional machines if the total consists of all setups, machine cycle times, load$/$unload times, and part transfer times between machines? $($b$)$ What is the total time to produce one of these parts using the CNC machining center if the total consists of the setup time, programming time, machine cycle time, and load$/$unload time. What are the percent savings in total time compared to your answer in $($a$)?($c$)$If the same part is produced in a batch of $20$ pieces, what is the total time to produce them under the same conditions as in $($a$)$ except that the total material handling time to carry the $20$ parts in one unit load between the machines is $40$ min? $($d$)$ If the part is produced in a batch of $20$ pieces on the CNC machining center, what is the total time to produce them under the same conditions as in part $($b$),$ and what are the percent savings in total time compared to your answer in $($c$)?($e$)$ In future orders of $20$pieces of the same part, the programming time will not be included in the total time because the part program has already been prepared and saved. In this case, how long does it take to produce the $20$ parts using the machining center, and what are the percent savings in total time compared to your answer in $($c$)?$