The process plan for a cast part specifies that two rough cuts and one finish cut be face$-$milled

on a vertical machining center. The casting is $60$ cm long, and the face mill has a diameter of

$10$ cm and, hence, a contact length of $5$ cm $.$ The speed of the casting on the machining center is

$250m\frac{m}{m}in$ for the rough cut and $175m\frac{m}{m}in$ for the finish cut. The time to load the casting

is $16$ sec $,$ and the unload time is $8$ sec $.$ The shop operates two shifts $5$ days a week for $48$

weeks a year. Each shift has $7\mathrm{.}5$ hours of available operating time. Operators can tend two

vertical machining centers at once without delaying the cycle time. If the demand for the cast

parts is $200,000$ per year, the number of vertical machining centers and operators is most

nearly:

O A$.2$ machining centers and $1$ operator

O B$.2$ machining centers and $2$ operators

O C$.8$ machining centers and $8$ operators

O D$.10$ machining centers and $10$ operators