Healthy Animals
Ryan is concerned about the diet he is feeding his pet. A nutritionist has recommended that the pet's diet
include at least 30 grams of protein and at least 16 grams of fat per day.
Ryan has two types of foods available - Food A and Food B. Each ounce of Food A supplies 2 grams of protein
and 4 grams of fat, while each ounce of Food B supplies 6 grams of protein and 2 grams of fat. Ryan's pet
should not eat a total of more than 12 ounces of food per day.
Ryan would like to vary the diet for his pet within these requirements, and so he needs to know what his
options are. Which combination of foods allows his pet to eat the most food possible?
1.
Choose variables to represent the amount of each type of food Ryan will include in the daily diet. State
clearly what the variables represent.
2. Use your variables to write inequalities to describe the constraints of the problem. What is the
objective function?
3.
Graph the feasible region.
4. What are the 4 corner points to your feasible region (Hint: Where does your protein and total food
lines cross? Where do your fat and protein lines intersect? Use a system of equations to solve.)
5. Which combination of food allows his pet to eat the most food per day?