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Topic: Uhhh....elp?
Replies: 2   Last Post: Apr 24, 1998 3:13 PM

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Dave Slomer

Posts: 244
Registered: 12/6/04
Posted: Apr 22, 1998 8:52 PM
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Here's a problem for ya:

The fixed costs of running a certain business are $16000 per month.
The cost of x hours of employee work is $28x.
The company brings in $(132+.01x) for the xth person-hour worked in a month.
Last month, the employees worked 10000 person-hours.
What is the average value of the profit per person-hour?

(...from Dick and Patton, Calc of a Single Var, section 7.3.)

I'm having a hard time with interpreting the "$(132+.01x) for the xth
person-hour worked in a month". I'm tempted to add, summing (132+.01x) over
whole numbers (and figuring revenue and profit from there), but why stop at
whole hours--why not tenths of hours or minutes? Looking at it differently,
why not just sum every thousand hours? (There's a HUGE difference, is why,
leading me to think about dividing (or multiplying) by something, but what
and why? I wonder if there's a delta-something I'm ignoring, which would
tell me what to divide (or multiply) by. But........)

The facing page has a new concept (to me), called "moving (weighted) average
of a function over period A" (defined as 1/A times the integral of f over
[x-A,x]) which I plan to use as my next tool, but time's a-wastin', so I'm
a-hollerin' "HEP!" in case that doesn't pan out, either. I can't see getting
any further with it since it's going to involve the same interpretation, I

BTW, in my version of the text (different from the kids' slightly later
editions), the $16000 figure is not mentioned, replaced by an hourly figure,
so it's not been a stable problem, and maybe needs another change.

Either a solution or an interpretation of the quoted sentence or a revision
of the problem (added fact?) would be greatly appreciated. Even an answer. I
got around $150 earlier. I don't even know if that's reasonable!

Over the years, I've learned that some problems require additional
assumptions NOT AT ALL clearly stated in the givens (e.g., ignore waste).

Help? Especially from you thousands of D&P users!

Dave Slomer
AP Calculus and computer science teacher
Winton Woods HS, Cinti, OH 45240

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