Given the following data points for a quadratic average cost function, determine the coefficients and the total cost function: (30, 400), (50, 250), (60, 550).

Here are the solutions to the problems:

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: Quadratic Cost Function

The average cost (AC) function is quadratic, so it can be represented as $AC = aQ^2 + bQ + c$, where $Q$ is the output.
We are given three data points:

1. For the 30th unit, $AC = N400$. So, $(Q=30, AC=400)$.
2. For the 50th unit, $AC = N250$. So, $(Q=50, AC=250)$.
3. For the 60th unit, $AC = N550$. So, $(Q=60, AC=5