Table D.3
Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible.She has decided to make her own cat food and has the following nutritional guidelines.Each four ounce portion must contain 22 units of protein,15 units of vitamin A,and 8 units of vitamin B.She has eggs,tomatoes,and chicken meat as possible inputs to her cat food.Each ounce of eggs contains 6 units of protein,4 units of Vitamin A,and 3 units of Vitamin B.Each ounce of tomatoes contains 1 unit of protein,8 units of Vitamin A,and 14 units of Vitamin B.Each ounce of chicken contains 22 units of protein,14 units of Vitamin A,and 8 units of Vitamin B.Chicken costs 40 cents per ounce,tomatoes cost 5 cents per ounce,and eggs cost 12 cents per ounce.
-Referring to Table D.3,what is an appropriate constraint for this scenario?
A)4*Eggs + 8*Tomatoes + 14*Chicken ≤ 15
B)4*Eggs + 8*Tomatoes + 14*Chicken ≥ 15
C)4*Eggs + 8*Tomatoes + 14*Chicken = 15
D)15*VitaminA = Eggs + Tomatoes +Chicken

Question

Quizplus · Accepted Answer

The constraint should ensure that each four ounce portion contains at least 22 units of protein, 15 units of vitamin A, and 8 units of vitamin B. To determine the amount of each input needed, we can set up the following equations:
6E + T + 22C >= 22 (protein)
4E + 8T + 14C >= 15 (vitamin A)
3E + 14T + 8C >= 8 (vitamin B)
Multiplying each equation by 4 (to account for the four ounce portion size) and adding them together, we get:
24E + 32T + 88C >= 88 (protein)
16E + 32T + 56C >= 60 (vitamin A)
12E + 56T + 32C >= 32 (vitamin B)
Simplifying, we get:
4E + 8T + 14C >= 15
Therefore, the appropriate constraint is 4*Eggs + 8*Tomatoes + 14*Chicken ≥ 15.

Table D.3 Lisa Lives Out in the Country with Her Seven Cats