Question 175391This question is from textbook Blitzer College Algebra
: As a manager of a financial planning business you have two financial planners, Phil and Francis. In an hour, Phil can produce either one financial statement or answer 8 phone calls, while Francis can either produce 4 financial statements or answer 10 phone calls. Does either person have an absolute advantage in producing both products? Should these two planners be self-sufficient (each producing statements and answering phones) or specialize? Be sure to show your work.
All help is appreciatted
This question is from textbook Blitzer College Algebra
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i would say francis has a definite advantage over phil.
phil can produce 1 financial statement while francis can produce 4.
phil can answer 8 phone calls while francis can answer 10 phone calls.
francis is definitely faster and therefore more productive assuming that the quality of the work that francis produces is at least equal to the quality of the work that phil produces.
given the same quality, francis has an absolute advantage over phil.
can anything be gained by specializing?
let's see:
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case 1:
phil does financial statements and francis does phone calls.
result is 1 financial statement and 10 phone calls completed per hour.
by the end of an 8 hour day you have:
8 financial statements completed and 80 phone calls answered.
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case 2:
phil does phone calls and francis does financial statements:
result is 4 financial statments and 8 phone calls completed per hour.
by the end of an 8 hour day you have:
32 financial statements and 64 phone calls completed.
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case 3:
phil does financial statements for 4 hours and francis does financial statements for 4 hours with the rest of the time being consumed by phone calls.
result is 20 financial statements and 72 phone calls completed.
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if you let francis be the benchmark of efficiency, then the results for each of these cases is:
financial statements benchmark = 32 financial statements per day.
phone call benchmark = 80 phone calls per day.
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with case 1:
8/32 = 25% efficiency for the statements
80/80 = 100% efficiency for the phone calls
with equal weighting, the overall efficiency for the day would be:
62.5%
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with case 2:
32/32 = 100% efficiency for the statements
64/80 = 80% efficiency for the phone calls
with equal weighting, the overall efficiency for the day would be:
90%
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with case 3:
20/32 = 62.5% efficiency for the statements
72/80 = 90% efficiency for the phone calls
with equal weighting, the overall efficiency for the day would be:
76.25%
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with equal weighting, it appears that letting francis do the financial statements would be the most in overall efficiency since she is 4 times as fast as phil in completing the financial statements while she is only 1.25 times as fast as phil in answering phone calls.
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weighting is a judgment call.
is completing a phone call more important than completing a financial statement?
if so, how much more?
what kind of weight should be applied?
this will most definitely change the result depending on the weighting factor applied.
as an example, assume a weighting factor for phone calls of 5 meaning phone calls are 5 times more important than completing a financial statement.
this could mean that when computing overall efficiency, you take 1 times the efficiency for completing the financial statement and 5 times the efficiency for completing phone calls when computing the average.
overall efficiency in the 3 test cases would be:
case 1:
1 times 25% plus 5 * 100% / 6 = 525/6 = 87.5%
case 2:
1 times 100% plus 5 * 80% / 6 = 500/6 = 83.333...%
case 3:
1 times 62.5% plus 5 * 90% / 6 = 512.5/6 = 85.4....%
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with equal weighting case 2 was the winner.
with weighting chosen as 5* for phone calls, case 1 was the winner.
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bottom line:
weighting has a definite impact.
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with equal weighting, it appears letting francis do the financial statement is the proper choice.
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is there a maximum mix other than letting francis do the financial statements all day?
let's see:
case 4:
phil does financial for 1 hour
francis does phones for 1 hour.
by the end of the day:
29 financial statements / 32 = 90.625% efficiency
66 phone calls / 80 = 82.5% efficiency
overall efficiency with equal weighting = 86.56%
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this is less than the 90% if we let francis do financial statements all day.
since the more phil does financial statements the less overall efficiency we get (case 3 was less than case 4) then we can safely assume that letting francis do the financial statements all day would be the most efficient, given equal weighting.
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answer is:
given equal weighting, i would say:
let francis do the financial statements.
let phil do the phone calls.
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assuming there is weighting to be applied, then the answer depends on the weight given to each.
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