>>1322607>>1322614Nevermind, this is wrong. The total cost of the machine you pay per year when you replace the machine every "t" years is (10000 + 100t^(7/4)) / t. Every "t" years you pay the cost of the new machine AND the total repair cost. Do it once every 5 years, you pay (new machine cost + total repair cost) / 5. And so on. I was incorrectly thinking you pay one or the other.
So, when is this minimized? It's going to be when the function stops decreasing and starts increasing, or when the derivative is 0.
(10000 + 100t^(7/4)) / t = 10000/t + 100t^(3/4)
The derivative is -10000/(t^2) + 75t(-1/4). The cost is minimized when this is equal to 0.
75t(-1/4) = 10000/(t^2)
75t^(7/4) = 10000
t^(7/4) = 133.33
t = 133.33^(4/7) = 16.378.
That's the correct answer, I believe. Sorry about earlier.
