SOLUTION: This is the first week of this class and it is not starting out good for me so far. Could you please help me with this problem? As a manager of a financial planning business you

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Question 175052This question is from textbook college algebra/ blitzer
: This is the first week of this class and it is not starting out good for me so far. Could you please help me with this problem?
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 10 phone calls, while Francis can either produce 3 financial statements or answer 12 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? Please show your work if possible. Thanks in advance. This question is from textbook college algebra/ blitzer

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What I would do is pick an arbitrary number
of financial statements that need to be filed by each
and phone calls that need to be made by each
f+=+20
p+=+200
The time in hours for each person to do these numbers of jobs is
t%5BPhil%2Cf%5D+=+20%2F1
t%5BPhil%2Cp%5D+=+200%2F10
and
t%5BFran%2Cf%5D+=+20%2F3
t%5BFran%2Cp%5D+=+200%2F12
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Now I need to look at the various ways they can work and arrive
at the least time to get the same amount of work done.
--------------------
Each doing both kinds of jobs until they are done:
t%5BPhil%2Cf%5D+%2B+t%5BPhil%2Cp%5D+=+20%2F1+%2B+200%2F10
20%2F1+%2B+200%2F10+=+40 hrs
and
t%5BFran%2Cf%5D+%2B+t%5BFran%2Cp%5D+=+200%2F12+%2B+20%2F3
20%2F3+%2B+200%2F12+=+70%2F3
70%2F3+=+23.33 hrs
So they did a total of 400 phone calls and 40 files done in 63.33 hrs
--------------------
Phil doing calls and Fran doing files:
t%5BPhil%2Cp%5D+=+400%2F10
t%5BPhil%2Cp%5D+=+40
t%5BFran%2Cf%5D+=+40%2F3
t%5BFran%2Cf%5D+=+13.33
So they did a total of 400 phone calls and 40 files done in 53.33 hrs
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Phil doing files and Fran doing calls:
t%5BPhil%2Cf%5D+=+40%2F1 hrs
t%5BFran%2Cp%5D+=+400%2F12
t%5BFran%2Cp%5D+=+33.33 hrs
So they did a total of 400 phone calls and 40 files done in 73.33 hrs
--------------------
This gives me a ranking and it looks like
Phil doing calls and Fran doing files is the
most efficient way for them to work
Fran is more efficient at doing both