00:02
A square -endons manufacturer allocates at least 2 ,400 units production time per day to make baseballs and footballs.
00:10
It takes 20 units of time to make a baseball and 30 units of time to make a football.
00:14
If x represents the number of baseballs made and y represents the number of footballs made, the graph of 20x plus 30y is greater than are equal to 2 ,400, shows the possible ways to schedule the production time.
00:30
Graph the inequality, then find three possible combinations of production time for the company to make baseballs and footballs.
00:40
Okay, so to graph an inequality, if we can write that in the form of y equals x plus b, then we can graph a straight line.
00:48
And so the first thing i'm going to do is i am going to take and rearrange that equation and solve it for y.
00:57
Okay, so first step, subtract 20x from both sides.
01:07
So that'll be gone and you'll get 30y is greater than or equal to minus 20x plus 2 ,400.
01:22
And as long as you're not multiply or dividing by a negative number, you don't have to worry about changing your sign.
01:30
So next step, i'm going to divide both sides 3 by 30.
01:41
So i'm going to get y is greater than it equal to.
01:46
Minus 20x over 30 would be a minus 2 thirds x and then 2 ,400 over 30.
01:55
Your zeros are canceled out.
01:57
I guess i should have done that right there, but the zeros are canceled out, so you have 240 over 3, which would be 80.
02:09
And so now you have something in the form of y equals mx plus b.
02:15
And since we know that our y intercept is 80, and it might be good to do these lines in, say, units of 10.
02:33
And since we're talking about production, we're really only talking about the positive x and positive y area.
02:46
So if each line represents 10, and this would be 20, 40, 60, 80, 100.
03:18
Okay, and then our y intercept is 80.
03:26
Right there and our slope is negative two thirds so you can think that and that is down to right three and we don't have to go by single units we can go by tens if we want so i could go down to 60 and then so down two it would be down one two lines and then right one two lines right one two lines right one two lines and right one two three lines down one two lines down one two lines oops, let me put one there.
04:03
And then write one, two, three lines, and then down one, two, lines, and write one, two, three lines from there.
04:16
And that would be 120 there.
04:20
Okay, so when you are talking about an inequality, you've got to realize that you need to look at the area that is included in the greater than or equal to area.
04:34
And sometimes it's, you're not 100 % sure if you're doing above a below the line.
04:42
My thought is it's going to be everything above that red line.
04:46
But just to verify that, if you take and plug in a number into our equation, and you can make it an easy number, like, for instance, if you put in the origin would be in that, so you could put in zero, zero.
05:03
So i'm just going to say try zero.
05:07
So if you say zero is greater than what equal to, negative two -thirds times zero be zero plus 80, then you would be saying zero is greater than equal to 80.
05:20
Is that true? no, it's not.
05:24
Zero is less than 80, so that's not true...