00:01
So here we're given a total cost function, which is equal to c of q, and that total cost function is 12 plus 10q minus 2 q squared plus q to the cubed over 3.
00:15
Right.
00:16
So for number one, what we need to do is average variable cost.
00:21
Well, that's equal to variable cost over q, right? this is my variable cost.
00:27
It is the part of the cost function that varies.
00:30
With q, right? the 12 is the fixed cost.
00:33
It does not vary with q, right? as q changes, that 12 just sits there.
00:39
So the average variable cost here would be 10 q minus 2 q squared plus q cubed over 3, all over q, which would be equal to 10 minus 2q minus q squared over 3.
00:57
Is that one of the options? yes, that is option c.
01:09
Great.
01:09
So for two, we're told about the marginal cost.
01:13
The marginal cost is the derivative of total cost with respect to the quantity.
01:17
So we need to apply the power rule.
01:19
The derivative of 12 is zero.
01:21
The derivative of 10q is 10.
01:23
The derivative of 2q squared is minus 4q.
01:26
And the derivative of q cubed over 3 is equal to q squared, right? is that one of the functions that we have available? again, it's starting with a 10.
01:39
I'm looking for a 4q.
01:41
That looks like function b.
01:43
Great.
01:44
And then finally, we're thinking about three.
01:47
We're told that the price is equal to six.
01:50
If the price is fixed at six, this is also the marginal revenue.
01:53
It doesn't matter how many we get.
01:55
The price is always six.
01:56
So the revenue from one more is always six.
01:58
We want to set marginal revenue equal to marginal cost...