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 $0.05 per 1,000 units collated. Required:
A. Determine the total costs of collating 500,000 and 1,700,000 per month:
1. With student help.
2. With the collating machine.
B. Determine the monthly volume at which the automatic process becomes preferable to the manual process.

A. The total costs of collating 500,000 per month With student help is $900

The total costs of collating 1,700,000 per month With student help is $3,060

The Total costs of collating 500,000 per month With the collating machine is $1,575

The Total costs of collating 1,700,000 per month With the collating machine is $1,635

B. The monthly volume at which the automatic process becomes preferable to the manual process is 885,714

Explanation:

A. In order to calculate the total costs of collating 500,000 and 1,700,000 per month With student help we would have to make the following calculations:

total costs of collating 500,000 per month With student help=(number of copies to be collating/average of copies per hour)*price per hour

total costs of collating 500,000 per month With student help=(500,000/5,000)$9

total costs of collating 500,000 per month With student help=$900

total costs of collating 1,700,000 per month With student help=(1,700,000/5,000)*$9

total costs of collating 1,700,000 per month With student help=$3,060

In order to calculate the total costs of collating 500,000 and 1,700,000 per month With the collating machine we would have to make the following calculations:

total costs of collating 500,000 per month With the collating machine= lease and operating costs+(number of copies to be collating/units collated)*additional price

Total costs of collating 500,000 per month With the collating machine= $1,550+(500,000/1,000)*$0.05

Total costs of collating 500,000 per month With the collating machine= $1,575

Total costs of collating 1,700,000 per month With the collating machine= $1,550+( 1,700,000/1,000)*$0.05

Total costs of collating 1,700,000 per month With the collating machine= $1,635

B. In order to calculate the monthly volume at which the automatic process becomes preferable to the manual process we would have to use the following formula:

the monthly volume at which the automatic process becomes preferable to the manual process is cost with students help=cost with collating machine

Therefore, (x/5,000)*$9=$1,550+(x/1,000)*$0.05

$8,750x=$7,750,000,000

x=885,714

The monthly volume at which the automatic process becomes preferable to the manual process is 885,714