Answer:
The company use 0 ounces of chicken and 100 ounces of grain in each bag of dog food in order to minimize cost.
Step-by-step explanation:
Let x be the number of ounces of chicken
let y be the number of ounces of grains
We are given that Chicken has 10 grams of protein and 5 grams of fat per ounce.
Chicken has protein in 1 ounce = 10
Chicken has protein in x ounces = 10x
Chicken has fat in 1 ounce = 5
Chicken has fat in x ounces = 5x
We are also given that grain has 2 grams of protein and 2 grams of fat per ounce
Grain has protein in 1 ounce = 2
Grain has protein in y ounces = 2y
Grain has fat in 1 ounce = 2
Grain has fat in y ounces =2y
Now we are given that . A bag of dog food must contain at least 200 grams of protein and at least 150 grams of fat.
So, equation becomes:
---A
---B
Since x and y represent the ounces .
So,
---C and
----D
Plot A ,B ,C and D on the graph
Refer the attached graph so , the corner points are (0,100),(10,50) and (30,0)
We are also given that chicken costs 10 cents per ounce and grain costs 1 cent per ounce
So, Cost function becomes : ![c=10x+y](https://tex.z-dn.net/?f=c%3D10x%2By)
At(0,100)
![c=10x+y](https://tex.z-dn.net/?f=c%3D10x%2By)
![c=10(0)+100](https://tex.z-dn.net/?f=c%3D10%280%29%2B100)
![c=100](https://tex.z-dn.net/?f=c%3D100)
At(10,50)
![c=10x+y](https://tex.z-dn.net/?f=c%3D10x%2By)
![c=10(10)+50](https://tex.z-dn.net/?f=c%3D10%2810%29%2B50)
![c=150](https://tex.z-dn.net/?f=c%3D150)
At(30,0)
![c=10x+y](https://tex.z-dn.net/?f=c%3D10x%2By)
![c=10(30)+0](https://tex.z-dn.net/?f=c%3D10%2830%29%2B0)
![c=300](https://tex.z-dn.net/?f=c%3D300)
Minimum cost is 100 cents at (0,100)
So, the company use 0 ounces of chicken and 100 ounces of grain in each bag of dog food in order to minimize cost.