September 7th, 2010 
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Replacement Copier
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Here is the question:
A high speed office copier has an initial price of $800. A service contract cost $160 for the first year and increase by $100 per year thereafter. It can be shown that over x years the total cost of the copier is given by:
C(x) = 800 + 110x + 50 x^2
When is the average cost per year smallest? (This is often referred to as the replacement time for a piece of equipment.) Answer in units of years.
Please let me know how to do the problem.
Or, a different approach:
If the total cost after x years is given by C(x), the average cost will be C(x)/x
C(x)/x = 800/x + 110 + 50x = AC(x) (average cost)
you can plot this to find the min, or differentiate:
AC ' = -800/x^2 + 50
set AC' = 0 so 50 = 800/x^2
x^2 = 800/50 = 16
x = 4
so at 4 years, the average cost will be at a minimum (verified from graph) = 510 / year
C(4) = 800 + 440 + 50(16) = 2040
AC(4) = 2040/4 = 510
AC " = 1600 / x^3
AC " is positive at x = 4, so this is a minimum
And since there is only one local extreme of the average cost function, this will also be the absolute minimum
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HP PHOTOSMART C4180 MAC Installion Software Download?
I bought this from jnr music world and the mac disc fell and got horribly scratched. Now i'm trying to install the software to use on my macbook bro and to no avail. I tried hp's website no luck there. Called customer service and they want to charge me a $24 plus shipping & handling for a replacement disc. Plz anywho knows where i can get the installation software to download? I'd hate to think i wont be able to use my all in one printer scaner copier =(
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