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 think.
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).