00:01
So we're told that yofc receives a shipment of 400 cases of specialty perfume early monday morning of every week, and they sell this at a rate of about 80 cases per day through monday to friday.
00:22
What we want to do is find the daily inventory or yofc.
00:29
And the hint we're given is to find a function that represents the inventory, and then integrate this.
00:36
So let's see what we have for inventory.
00:41
So we can write an inventory function based off.
00:49
So let's see what we're told.
00:51
We're told that they start with 400 cases monday morning.
00:56
So this can kind of be thought of as our intercept.
01:02
So 400.
01:02
And then it says they sell the perfume at a rate of about 80 cases per day.
01:15
So minus 80.
01:20
And what we're going to mean by this is d equals 1.
01:25
So d is equal to 0 is start of monday.
01:35
D is equal to 1 is end of monday.
01:44
D equals 2 is end of tuesday and so on and so forth.
01:57
So d is equal to 5 would be the end of friday.
02:00
D equals 5 is end of friday.
02:11
And if we were to plug 5 into here, we would end up getting zero for our inventory.
02:16
So that would kind of make sense for our equivalent.
02:20
We start with 400 when we plug in 0, and when we plug in 5, we end up with all of our inventories.
02:26
Which is what we would hope to happen.
02:30
Now that we have this inventory function, so i'm going to call this function i of d.
02:41
So inventory depending on the day.
02:44
Well, if we want to find the average, so average on, so what we're doing is we're taking integral or we're trying to find the average on this interval here zero or monday to friday which the start of monday is zero and then the end of friday is going to be five so we have an average on zero to five of so remember what we want to do is one over five minus zero integrated from and you maybe i should put the 5 in 0 in blue...