00:02
Okay, in this problem, you are given some information about manufacturers and their fixed costs, as well as the cost per widget.
00:11
So for part a, you are told that this manufacturer has a fixed cost of $2 ,000 and that the cost per widget is $20.
00:20
Because c always increases by $20 when n is increased by 1, that would mean that c has a constant rate of change and is a linear function of 1.
00:32
So every time you make another widget, the cost goes up by $20.
00:39
That $20 is what we would call the slope.
00:46
And the initial value is that $2 ,000, which is our fixed costs.
00:55
If we want to write a formula, we want to think about the format for a linear function.
01:07
And our format for those usually follows y equals mx plus v, where the m is.
01:12
The slope and the b is our initial value.
01:16
So for this first part, our formula would look like 20 plus 2 ,000.
01:30
In part b, you are told that it costs $12 per widget and that there's a total cost of $3 ,500 for 150 widgets.
01:39
So we don't know the initial value, which in our formula is the b of y equals mx plus b.
01:47
We do do.
01:48
Know that it costs $3 ,500, and it's $12 for each widget, and they made 150 widgets.
02:01
So using that setup, we can solve this equation for b.
02:07
And in order to do that, we need to multiply 12 by 150, which gives us 1 ,800.
02:20
And then to solve for b, which again is the fixed cost for this manufacturer, we can subtract that from the other side.
02:31
Which would give us $1 ,700.
02:37
For part c, we're told about another manufacturer, and we know that the total cost is $3 ,300 when they make 100 widgets, and that the total cost is $4 ,300 when they make 150 widgets.
02:52
We don't know how much it costs per widget, and we don't know the fixed costs.
02:59
But we can use our setup of y equals mx plus b to put the numbers that we do know in place...