Question

A hog producer is feeding soybean meal and corn to his pigs. He needs to know how many pounds he needs to feed of each in order to meet his pig’s crude protein requirements. Feed 1, soybean meal has a 45 percent crude protein and feed 2, corn has a crude protein percent of 15 percent. The desired crude protein percent for the pigs is 25 percent. Calculate how many pounds of each feed the hog producer will need to feed his pigs. In this example, 1 ton (2,000 lbs.) of feed is needed

Answer 1

The hog producer will need to feed approximately 666.67 pounds of soybean meal and 1333.33 pounds of corn to meet the pigs' crude protein requirements.

Step-by-step explanation:

To calculate how many pounds of each feed the hog producer will need to feed his pigs, we can set up a system of equations.

Let x be the number of pounds of feed 1 (soybean meal) and y be the number of pounds of feed 2 (corn).

We can set up the following equations based on the crude protein requirements:

x + y = 2000 (since 1 ton is 2000 pounds)

0.45x + 0.15y = 0.25 * (x + y)

Simplifying the second equation, we get:

0.45x + 0.15y = 0.25x + 0.25y

0.2x = 0.1y

2x = y

Substituting y with 2x in the first equation:

x + 2x = 2000

3x = 2000

x = 2000/3 ≈ 666.67 pounds

Finally, we can substitute the value of x back into the second equation to find the value of y:

0.45 * (2000/3) + 0.15y = 0.25 * (2000/3 + y)

900/3 + 0.15y = 500/3 + 0.25y

400/3 = 0.1y

y = (400/3) / 0.1 ≈ 1333.33 pounds

Therefore, the hog producer will need to feed approximately 666.67 pounds of feed 1 (soybean meal) and 1333.33 pounds of feed 2 (corn) to meet the pigs' crude protein requirements.

Answer 2

Feed 1, Soybean meal required =
`(2000)/(3) \text{ lbs.}`

Feed 2, Corn meal required =
`(4000)/(3) \text{ lbs.}`

Step-by-step explanation:

Total feed is 1 ton i.e. 2000 lbs.

Let x be the amount of Feed 1 required.

Feed 1 has
`45\%` of protein.

`\text{Protein in Feed 1 = }x * (45)/(100) ..... (1)`

Then, amount of Feed 2 required =
`(2000 - x) \text{ lbs.}`

Feed 2 has
`15\%` of protein.

`\text{Protein in Feed 2 = }(2000 - x) * (15)/(100) ..... (2)`

As per question, total protein required is
`25\%` of 2000 lbs .

Adding (1) and (2) and putting it equal to total protein required.

`\Rightarrow x * (45)/(100) + (2000 - x) * (15)/(100) = 2000 * (25)/(100)\\\Rightarrow 45x + 30000 - 15x = 50000\\\Rightarrow 30x = 20000\\\Rightarrow x = (2000)/(3)`

Feed 1 required =
`(2000)/(3)\text{ lbs .}`

Feed 2 required =
`2000 - (2000)/(3)\\`

`\Rightarrow (4000)/(3)\text{ lbs.}`