If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost?

Question

Nutrition   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 222 grams of protein and at least 152 grams of fat. If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.)

grain oz= ?

chicken oz= ?

Answer 1

Well suppose x = oz of chicken and y = oz of grain

x >= 0 (1)

y > = 0 (2)

Protein : 10x + 2y >= 222 (3)

Fat : 5x + 2y >= 152 (4)

Cost = 9x + 1y

So to solve this plot the four lines (1) - (4) on Desmos [ replace the inequality sign with = ]

The feasible region will be the area above line (3) and line (4).

Calculate the cost at the intersection of lines (3) and (4). This will be the minimum cost, and (x,y) at that point tells you the required mix. You should find x=14, y =41.