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

Answer:

Feed 1, Soybean meal required =  $\dfrac{2000}{3} \text{ lbs.}$

Feed 2, Corn meal required = $\dfrac{4000}{3} \text{ lbs.}$

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.

$\text{Protein in Feed 1 = }x \times \dfrac{45}{100} ..... (1)$

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

Feed 2 has $15\%$ of protein.

$\text{Protein in Feed 2 = }(2000 - x) \times \dfrac{15}{100} ..... (2)$

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

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

$\Rightarrow x \times \dfrac{45}{100} + (2000 - x) \times \dfrac{15}{100} = 2000 \times \dfrac{25}{100}\\\Rightarrow 45x + 30000 - 15x = 50000\\\Rightarrow 30x = 20000\\\Rightarrow x = \dfrac{2000}{3}$

Feed 1 required = $\dfrac{2000}{3}\text{ lbs .}$

Feed 2 required = $2000 - \dfrac{2000}{3}$

$\Rightarrow \dfrac{4000}{3}\text{ lbs.}$