00:01
Okay, let x be the number of a things that you make and y be the number of b things that you make.
00:09
Okay, we know that the sales of a is at least, that at least goes there, at least 80 % of b.
00:17
So x is greater than or equal to 0 .80y.
00:24
Okay, the at least says it's either equal to 80 % or it is more than.
00:30
So that's why i use greater than or equal to.
00:33
They cannot sell more than 110a.
00:37
So x has to be less than or equal to 110.
00:42
They can't sell more than that.
00:46
The raw materials, it takes two pounds for each a, four pounds for each b, and they have 300 pounds total.
00:53
So they're making xas.
00:56
So that's going to be 2x for the raw materials to make the a's.
01:01
They're making y number of bs and they cost they're four pounds for each b so that would be four y pounds and they have only 300 so that has to be less than or equal to 300 doesn't have to equal 300 it could be less than they maybe don't use it all each time all right we're going to maximize the profit 400 i guess it's indian rupees so 400 for each a so the profit is 400 times x plus 900 b's so 900 y all right so next what you have to do is graph it okay but i'm not very fussy about the graphing we just need to get it in the right place so let's start with x is greater than or equal the point eight y okay if you think about it as a line x equals 8t's y or y 10 8x.
02:14
Okay, it goes through 0 -0 because it's y intercept is 0.
02:18
And a slope is 10 -8, so it's going to go uphill.
02:21
So i'm just going to draw it like this.
02:25
Okay, so that's y equals 10 -8x.
02:34
Okay, next, x has to be less than or equal to 110.
02:39
So x equals 110.
02:42
That's a vertical line.
02:44
Let's put it right here.
02:50
Oh, i forgot to do.
02:50
The shading on the first one.
02:52
Well, let's go ahead and do the shading on the second one.
02:54
X has to be less than 110.
02:57
Okay, so that's that way.
03:00
Okay, on the first one, x had to be greater than or equal of 0 .80y.
03:06
So let's just pick a point.
03:07
Here's one.
03:10
Let's say it's 3 .0.
03:13
Is x bigger than y? yeah.
03:15
So on that one, we're going to go this way.
03:21
All right.
03:21
Now, the last one is 2x plus 4y less than or equal to 300.
03:28
Let's do this one in red.
03:36
So first let's graph the line if y equals zero, x is 150.
03:44
Okay, so that's going to be over here.
03:49
And if x equals 0, y equals 175.
03:57
So let's just stick it right here somewhere.
04:01
And that was x equals 150 there, y equals 75 there.
04:10
Okay, and then if we put the less than or equal to, if you try zero, zero, then zero plus zero less than or equal to 300.
04:19
So we're going to shade down that way.
04:22
Okay, so the area that we're interested in is this right here.
04:32
Okay, so we need to find this point, this point, this point, and this point.
04:37
And then plug them into our profit equation, and whichever one gives us the biggest profit is the number of a and b things we.
04:45
Should make.
04:47
Okay, well it's not going to be this one, but let's still find it.
04:50
Okay, i already know it.
04:51
It is zero zero.
04:54
Okay, and we know this one because i was so clever and labeled it.
04:57
That one's 110, 0...