Automatic versus Manual Processing

Assume Office Depot processes $2,500,000$ photocopies per month at its service center. Approximately $50\%$ of the photocopies require collating. Collating is currently performed by high school and college students who are paid $$10$ per hour. Each student collates an average of $5,000$ copies per hour. Management is contemplating the lease of an automatic collating machine that has a monthly capacity of $6,000,000$ photocopies, with lease and operating costs totaling $$3,000,$ plus $$0\mathrm{.}05$ per $1,000$ units collated.

$($a$)$ Determine the total costs of collating $1,000,000$ and $2,000,000$ per month:

$1.$ With student help.

$1,000,000$Answer $12,000,000$Answer $2$

$2.$ With the collating machine.

$1,000,000$Answer $32,000,000$Answer $4$

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

Round answer to the nearest whole number.$$

Answer $5$ copies