Question

A company offers ID theft protection using leads obtained from client banks. Three employees each work 40 hours a week on the leads. These employees are each paid $25 per hour. Each employee identifies an average of 3,000 potential leads a week. There are no duplications in these three lists. An average of 5 percent of the potential leads actually sign up for the service, paying a one-time fee of $70. Material costs are $1,000 per week, and overhead costs are $9,000 per week. Consider the output as the fees generated.

Calculate all productivity factors to three decimal places (x.xxx)

a) What are the labor hours productivity and the multifactor productivity for this operation?  

b) From the results in a suppose the company wants to improve the multifactor productivity by 10% by reducing the labor hours used. What must the reduction in labor hours per employee per week be to achieve this goal?

c) Use the original information in the problem to answer this part. Suppose the company realizes that its overhead costs were miscalculated. The company needs the multifactor productivity to be at least 1.25. While keeping all of the other values from the original information the same, what is the maximum value that the overhead costs per week can be to ensure the multifactor productivity is at least 1.25?

Answer 1

Output = 5% of 3000 * $70 * 3 = $31500

a)

Labor hour = 3*40 = 120 hours

Labor hour productivity = 31500/120 = $262.500 per labor hour

Multifactor input = 120*25 + 1000 + 9000 = 13000

Multifactor productivity = 31500/13000 = 2.423

b)

Let the labor hour be X

A 10% in improvement means the new multifactor productivity should be a 2.423*1.1 = 2.6653

Now we can equate it as

2.6653 = 31500/(3*25*X + 1000 + 9000)

X = (31500/2.6653 – 1000 – 9000)/75 = 24.247 hours

The reduction should be 40 – 24.247 = 15.753 hours per employee

c)

Let the overhead cost be X

Now we can equate it as

1.25 = 31500/(120*25 + 1000 + 9000 + X)

X = (31500/1.25 – 1000 – 9000 – 120*25)

X = 12200

A maximum of $12200 can be incurred as overhead cost