00:01
So in this question we're told that chicken has 10 grams of protein and 5 grams of fat per ounce and grain has 2 grams of protein and 2 grams of fat per ounce.
00:24
So that means that the amount of protein is 10 times the amount of chicken plus twice the amount of grain and the amount of fat is 5 times the amount of chicken plus 2 times the amount of grain.
00:43
Let's call this chicken and grain but the cost, so this is cost, fat, protein, the cost is 9 per ounce of chicken plus 1 cent per ounce of grain.
01:12
So how many ounces of each should ruff use to minimize cost? well we need at least 226 grams of protein and at least 166 grams of fat.
01:26
Well what we want to see is that we are going to need to saturate the inequalities.
01:41
So we want to saturate the inequalities since making there be more protein or more fat than necessary is just going to make things more expensive.
02:01
So actually what i'm going to do is i'm going to first write, so when the protein is saturated we have 10 chicken plus 2 grain equals 226.
02:20
So that means that grain is 226 minus 10 chicken divided by 2.
02:28
226 divided by 2 is 113 and then we have minus 5 times chicken.
02:37
So then the cost is going to be 9 chicken plus 1 grain so plus 113 minus 5 chicken which is 4 chicken plus 113.
02:55
So then we can look at the fat constraint that 5 chicken plus 2 grain has to be greater than 116.
03:01
That has to be greater than 116.
03:10
So we have 5 chicken minus 10 chicken is minus 5 chicken plus 226 greater than 116.
03:21
226 minus 116 is 110 and that has to be greater than 5 chicken.
03:30
So that means that we have to have less chicken than 110 divided by 5 which is 22.
03:37
But the cost is just 4 chicken plus 113.
03:43
So that means that minimizing cost just gives us that the chicken is equal to 0 and then the grain, remember that grain was equal to 113 minus 5 chicken, grain is going to be equal to 113 and then the cost is equal to 113 as well...