00:01
All right, so our job here is to analyze this cost function that we're given and answer a few questions.
00:06
So the first thing we're going to do is we're going to go ahead and determine the production level of producing 1 ,500 of a particular quantity.
00:14
To do this, we have to figure out how much it costs reduce 15 of 100 of these.
00:17
This is a very simple calculation.
00:20
We just go ahead and plug 1 ,500 in everywhere we see an x and divide through by those numbers.
00:26
Take a second to go ahead and calculate those values.
00:29
And what we'll get is the following.
00:31
Square of 1500 is about 38 .72 times that by 250, and you'll get 9 ,682 .46.
00:41
And then go ahead and calculate 1 ,500 squared.
00:44
That gives you about 2 .25 million.
00:47
Divide that by 42 ,875, and you get about 52 .478.
00:53
Add those two together, and you get $9 ,734.
01:03
To produce 1 ,500 of that item.
01:05
That's part a.
01:07
Part b wants us to find the average cost.
01:10
Well, the average cost is pretty nice to calculate.
01:13
It's just the total cost of producing 1 ,500, divided by the actual number of items produced, which equals 1 ,500.
01:25
So this is going to be c of 1 ,500, and we're going to divide it by 1 ,500.
01:30
So take your 9 ,734 .94, divide it by 1 ,500, and you get $6 ,000.
01:37
And $48, well in this case we went around, $0 .49 .0 .0.
01:44
That's the average cost per item.
01:47
Now, part c wants us to find the marginal cost.
01:51
Marginal cost is the derivative of cost.
01:54
It's how much it costs to produce one additional unit of that quantity.
01:58
So marginal cost is just going to be this derivative.
02:00
So calculate the derivative of cost.
02:03
And to do that, it's not that bad.
02:05
It's some power rules.
02:06
It becomes 125 over 2.
02:11
Pardon me.
02:16
So it does this way.
02:17
250 times 1 1ā2.
02:20
And then go ahead and do that by the power rule.
02:24
You get 2x divided by the constant, which you could have just pulled out.
02:28
And i think it wants us to calculate it at 1 ,500.
02:31
So simplify a little bit.
02:32
You get 125 over root x plus 2x over 4 ,000875.
02:39
Just calculate the value at 1 ,500 and we'll get the marginal cost.
02:42
Remember, the square of 1 ,500 here was about 38 .73...