Question

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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.
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Calculate all productivity factors to three decimal places (XXX)
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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 pait. 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 1.257​

Answer 1

a).

• Labor hours productivity=3.500

• Multi-factor productivity=2.423

b). The reduction in labor hours per employee per week to achieve this goal=15.735 hours

c). The maximum value that the overhead costs per week can be to ensure the multi-factor productivity is at least 1.257=$21,059.666

Step-by-step explanation:

a).

• Step 1: Determine the labor hours productivity

Labor output per week=potential leads×fee

where;

potential leads=5% of potential leads, and potential leads=3,000

potential leads=5%×3,000

potential leads=(5/100)×3,000=150

one-time fee=$70

replacing;

Labor output per week=70×150=$10,500

Labor input per week=cost per hour per employee×number of employees×number of hours worked

where;

cost per hour per employee=$25

number of employees=3

number of hours worked=40

replacing;

Labor input per week=25×3×40=$3,000

Labor hours productivity=labor output per week/labor input per week

Labor hours productivity=10,500/3,000=3.500

• Step 2: Determine the multi-factor productivity

Multi-factor productivity=Generated fees/(labor cost+material cost+overhead cost)

where;

generated fees=number of employees×potential leads×potential ratio×fee

number of employees=3, potential leads=3,000, potential ratio=5%=5/100=0.05, fee=$70

generated fees=3×3,000×0.05×70=$31,500

Labor cost=$3,000

Material cost=$1,000

Overhead cost=$9,000

Total cost=3,000+1,000+9,000=$13,000

replacing;

Multi-factor productivity=31,500/13,000=2.423

b). Increasing the multi-factor productivity (MP) by 10%

New MP=(110/100)×2.423=2.665

New MP=generated fees/labor cost+material cost+overhead cost

labor cost=cost per hour per employee×number of employees×number of hours worked

where;

cost per hour per employee=$25

number of employees=3

number of hours worked=h

labor cost=25×3×h=75 h

material cost=$1,000

overhead cost=$9,000

generated fees=$31,500

New MP=2.665

replacing;

2.665=31,500/{(75 h)+(1,000)+(9,000)}

2.665=31,500/75 h+10,000

2.665(75 h+10,000)=31,500

199.875 h+26,650=31,500

199.875 h=31,500-26,650

199.875 h=4,850

h=4,850/199.875

h=24.265

New labor hours=24.265 hours per week

Initial labor hours=40 hours per week

Reduction in labor hours=Initial labor hours-new labor hours

Reduction in labor hours=(40-24.265)=15.735

The reduction in labor hours per employee per week to achieve this goal=15.735 hours

c). Using a multi-factor of 1.257

MP=generated fees/labor cost+material cost+overhead cost

where;

MP=1.257

generated fees=$31,500

Labor cost=$3,000

Material cost=$1,000

Overhead cost=c

replacing;

1.257=31,500/(c+3,000+1,000)

1.257=31,500/c+4,000

1.257(c+4,000)=31,500

1.257 c+5,028=31,500

1.257 c=31,500-5,028

1.257 c=26,472

c=26,472/1.257=21,059.666

The maximum value that the overhead costs per week can be to ensure the multi-factor productivity is at least 1.257=$21,059.666