Answer:
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
Explanation:
a).
- <em>Step 1: Determine the labor hours productivity</em>
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
- <em>Step 2: Determine the multi-factor productivity</em>
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