Ruff Makes Dog Food Out of Chicken and Grain

Multiple Choice

Ruff makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat/ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 200 grams of protein and at least 50 grams of fat. If chicken costs 15 cents per ounce and grain costs 2 cents per ounce, how many ounces of each should Ruff use in each bag of dog food in order to minimize cost What are the shadow costs of protein and fat ?

A) 100 oz of chicken and no grain, 1 cents per gram of protein and 1 cents per gram of fat
B) 200 oz of chicken and no grain, 0 cents per gram of protein and 1 cents per gram of fat
C) 100 oz of chicken and no grain, 0.5 cents per gram of protein and 0.5 cents per gram of fat
D) 200 oz of grain and no chicken, 0.5 cents per gram of protein and 0.5 cents per gram of fat
E) 100 oz of grain and no chicken, 1 cents per gram of protein and 0 cents per gram of fat