Rome Petshop uses 3 different ingredients to manufacture 4 types of dog food. These 3 ingredients are protein, fat, and grains. Rome Petshop has 1000 pounds of protein, 750 pounds of fat, and 450 pounds of grains in its inventory for August 2020 production.

The four types are dogfood and their specifications are as follows.

Puppy-Love: At least 40% is protein, at least 30% is fat, no more than 10% is grain.

Muscle-Pooch: At least 55% is protein, no more than 15% is fat

Adult-K-nine: At least 30% is protein, at least 25% is grain

Senior-General: At least 30% is grain   

Each pound of Puppy-Love, Muscle-Pooch, Adult-K-Nine, Senior-General can bring in profit of $28, $33, $20, and $25, respectively. Since Muscle-Pooch was recently selected as the best pet food by an international pet magazine, it has a very high sales demand. Thus, at least 355 pounds of Muscle-Pooch must be manufactured. Rome Petshop need to find the most profitable way to manufacture these four types of dog food.