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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 $0.05 per 1,000 units collated.

Required:
a. Determine the total costs of collating 1,000,000 and 2,000,000 per month.
b. Determine the monthly volume at which the automatic process becomes preferable to (costs less than the manual process.

Respuesta :

Parrain

The total cost of collating 1,000,000 per month is:

  • With students = $2,000
  • With machine = $3,050.

The total cost of collating 2,000,000 per month is:

  • With students = $4,000
  • With machine = $3,100

The monthly volume at which the automatic process is preferred is 1,538,462.

What is the total cost of collating with students?

When collating 1,000,000, the cost is:

= 1,000,000 / 5,000 x $10 per hour

= $2,000

When collating 2,000,000, cost is:

= 2,000,000 / 5,000 x 10

= $4,000

What is the total cost of collating with the machine?

When collating 1,000,000, the cost is:

= (1,000,000 / 1,000 x 0.05 per thousand units ) + 3,000 operating cost

= $3,050

When collating 2,000,000, cost is:

= (2,000,000 / 1,000 x 0.05 per thousand units ) + 3,000 operating cost

= $3,100

What volume is the machine preferred?

Assume the volume is x:

(x / 1,000 x 0.05 per thousand units ) + 3,000 operating cost = x / 5,000 x 10

0.00005x + 3,000 = 0.002x

0.00195x = 3,000

x = 3,000 / 0.00195

= 1,538,462 photocopies

Find out more on total costs at https://brainly.com/question/14332852.

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