00:01
For this problem we're given the average cost, which is defined by c bar, and this average cost is in hundreds of dollars.
00:09
The first part is asking for the amount where the average cost approaches to as daily production increases.
00:18
That basically is just getting the limit of c bar as q approaches infinity.
00:24
So the limit, as q approaches infinity, for c bar, that's equal to the limit, as q approaches infinity of 324 over square root of q squared plus 35 plus 5 over q, plus 19 over 18, that's equal to 324 over we have infinity plus 5 over infinity, plus 19 over 18 and since constant over infinity approach to zero so this goes to zero as well as this and we have value equal to 19 over 18 dollars that is about 1 .06 for part b we want to find the manufacturer's marginal cost when 17 units are produced now since we're given the average cost you first want to find the total cost so you know total cost c is equal to c bar times q so this is just q times 324 over square root of q squared plus 35 plus 5 over q plus 19 over 18 that's equal to 324 q over square root of q squared of q squared plus 35 plus 5 plus 19 over 18 times q.
02:06
And now for the marginal cost, you simply take the derivative of c with respect to q.
02:11
We have marginal cost equal to dc over dq.
02:18
That's all you have to do, caution rule for the first term, that's square root of q squared plus 35 times 324, minus 324 q times 1 half times q squared plus 35 raised to negative 1 half times 2 k this divided by the square of the denominator which basically just gets rid of the radical so we have q squared plus 35 plus derivative of the constant, which is 0, plus derivative of 19 over 18, q is plus 19 over 18...