Automatic versus Manual Processing

Red Star Copy Service processes $2,100,000$ photocopies per month at its service center. Approximately $50$ percent of the photocopies require collating. Collating is currently performed by high school and college students who are paid $$9$ per hour. Each student collates an average of $5,000$ copies per hour. Management is contemplating the lease of an automatic collating machine that has a monthly capacity of $6,000,000$ photocopies, with lease and operating costs totaling $$1,550,$ plus $$0\mathrm{.}05$ per $1,000$ units collated.

$($a$)$ Determine the total costs of collating $500,000$ and $1,700,000$ per month:

$1.$ With student help.

$500,000$Answer $11,700,000$Answer $2$

$2.$ With the collating machine.

$500,000$Answer $31,700,000$Answer $4$

$($b$)$ Determine the monthly volume at which the automatic process becomes preferable to $($cost less than$)$ the manual process.

Answer $5$ copies