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 218 grams of protein and at least 168 grams of fat. If chicken costs 10¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food in order to minimize cost

Ruff should use 109 ounces of grain only in order to minimize cost.

Explanation:

For Chicken

Protein in Chicken = 10 grams of protein per ounce

Fat in Chicken = 5 grams of fat per ounce

Number of chicken ounce needed for protein = 218/10 = 21.8

Number of chicken ounce needed for fat = 168/5 = 33.6

Chicken cost = 10¢ per ounce

Cost of chicken required for protein = 21.8 * 10¢ = 218¢

Cost of chicken required for fat = 33.6 * 10¢ = 336¢

For Grain

Protein in Grain = 2 grams of protein per ounce

Fat in Grain = 2 grams of fat per ounce

Number of grain ounce needed for protein = 218/2 = 109

Number of grain ounce needed for fat = 168/2 = 84

Chicken cost = 1¢ per ounce

Cost of grain required for protein = 109 * 1¢ = 109¢

Cost of grain required for fat = 84 * 1¢ = 84¢

Conclusion

In order to minimize cost, Ruff should use 109 ounces of grain only in each bag of dog food to obtain at least 218 grams of protein and even more than 168 grams of fat.

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