9. 6 points My Notes Ruff, Inc. makes dog food out of chicken and grain. Chicken

Question

9. 6 points My Notes Ruff, Inc. makes dog food out of chicken and grain. 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. A bag of dog food must contain at least 236 grams of protein and at least 176 grams of fat. If chicken costs 9c per ounce and grain costs 1c per ounce, how many ounces of each should Ruff use in each bag of dog food in order to minimize cost? HINT [See Example 4.] (If an answer does not exist, enter DNE.) grain chicken oz 0Z

Explanation / Answer

Let proteins be 'P' and fat be 'F'

Given,

1 ounce of chicken=10 gms of proteins(10*P)+5 gms of fat(5*F)=9¢

1ounce of chicken=10P+5F=9¢ ------------> equation (1)

Similarly for grains, 1 ounce of grains=2P+2F=1¢ ---------------> equation (2)

Given one bag of dog food contains atleast 236 gms of proteins and 176 gms of fat.

Multiplying equation (1) with 14 and equation (2) with 53.

So equations becomes,

14 ounces of chicken=140P+70F=126¢ ----------------> equation(3)

53 ounces of grains=106P+106F=53 ¢-----------------> equation(4)

Add equation (3) and equation (4)

67 ounces of dog food bag =240P+176F=179¢

So,One bag of dog food contains 240 gms of proteins and 176 cms of fat which costs 179 ¢ requires 14 ounces of chicken and 53 ounces of grains.

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