00:01
This is a linear programming problem, meaning we need an objected function which is generally written as z.
00:07
The objective function is that equation we're trying to maximize, minimize, or optimizing general rules.
00:15
In this case, we're trying to minimize the cost per kilogram or the total cost of the production.
00:21
So we're given that feed number one costs 0 .25 per kilogram of that feed number one.
00:29
So x1 represents the number of kilograms for feet 1.
00:33
Feet 2 is 0 .30 times how many kilograms there are on feet 2.
00:39
Then feet 3, 0 .32 times that amount of kilograms.
00:44
And finally, we have feet 4, which is 0 .15 x4.
00:50
This is the objective function that we're trying to minimize, because we're trying to minimize this cost.
00:55
But we can't really do a linear programming problem with just an objective function because if we try to minimize this function, it's just going to be zero.
01:04
That's the minimum value.
01:05
We need to put some things that are called constraints, which are going to be the limitations of this.
01:11
The first constraint is that the total production has to equal 8 ,000 kilograms.
01:17
So x1 plus x2, plus x3, plus x4 have to equal 8 ,000 kilograms.
01:27
That's the first of the constraints because that's the total production.
01:32
The next constraint is related to the production.
01:35
The farmer is saying that 20 % of that production have to equal corn.
01:41
So if we are given the percentages of corn of 20%, 15%, 20%, and 10%, we have to write the equation related to corn.
01:51
So the constraint related to corn, let's put c, it goes like this...