# Math Help - Application of business calculus

1. ## Application of business calculus

Suppose a total cost function is given by TC=0.01Q2+5Q+100, where TC is total cost (£'s) and Q is output (units). Find the output level that minimises average total cost (ATC)

2. ## Re: Application of business calculus

Originally Posted by James127

Suppose a total cost function is given by TC=0.01Q2+5Q+100, where TC is total cost (£'s) and Q is output (units). Find the output level that minimises average total cost (ATC)
You don't really need to use calculus. Do you know how to find the turning point of a Quadratic?

3. ## Re: Application of business calculus

Yes, but the part that confuses me is that:

ATC = TC/Q

=0.01Q+5+100/Q

Where can you go from there with 100/Q?

Or am I confusing something that should be a lot simpler...

4. ## Re: Application of business calculus

I assumed that the function TC given was the Average Total Cost.

If ATC = TC/Q as you believe, then write 100/Q as 100Q^(-1). You should know how to differentiate a function of the form ax^n.

5. ## Re: Application of business calculus

total cost,

$C = 0.01Q^2 + 5Q + 100$

average total cost per unit,

$\bar{C} = 0.01Q + 5 + \frac{100}{Q}$

find $\frac{d\bar{C}}{dQ}$ , and use the first derivative test to determine the value of $Q$ that minimizes $\bar{C}$