Cat food is made from a mixture of three items: fish, shrimp, and grain. As an upstart pet food company, we only have two containers to store the three items. One container will hold both the fish and the shrimp, while the other container will contain the grain. Our company produces two types of cat food: Easy and Deluxe. Easy sells for $5.00 per pound, and Deluxe sells for $6.00 per pound. The composition of Deluxe must contain at least 20% shrimp and 10% fish, while the Easy mixture can contain no more than 80% grain. The per pound cost to acquire fish, shrimp, and grain is $1.50, $3.00, and $1.00, respectively. Additionally, there is 200 pounds of fish available for purchase, 100 pounds of shrimp, and 500 pounds of grain. Demand is known to be much greater than we can possibly produce, and so we can easily sell all of the cat food that we make. The goal is to maximize profit. Formulate the model for this problem and find the solution, stating the amount of Easy and Deluxe that should be produced, as well as the amount of raw material (fish, shrimp, and grain) that is used.
Need MAX or MIN formula and constraint.