Please...I really need help with this story problem. HELP!
Marks pet needs to eat at least 18 grams of fiber but less than 25 grams of protein each day. Mark gives his dog Food A and Food B throughout the day. Food A has 2 grams of fiber and 3 grams of protein in each serving. Food B has 4 grams of fiber and 1 gram of protein for each serving.
a. Write a system of inequalities that determine the maximum and minimum amount of each food Mark can give his pet each day. Will the amount of Food A or B ever be negative? Please account for this in your system of inequalities.
b. Give three solutions that would solve Marks pet needs. Show that each solution works.
2A+4B>18
3A+1B < 25
A>0
B>0
(A,B) = (1,5) …2(1)+4(5)>18 and 3(1)+1(5) < 25
(A,B) = (2,5) …2(2)+4(5)>18 and 3(2)+1(5) < 25
(A,B) = (3,5) …2(3)+4(5)>18 and 3(3)+1(5) < 25
If you copy and paste this solution, you will earn a 0 for plagiarism. Do your own work. Solve it a different way.
a. To determine the maximum and minimum amount of each food Mark can give his pet each day, we can use the following system of inequalities:
Let x represent the number of servings of Food A.
The fiber requirement can be represented by the inequality:
2x + 4y ≥ 18
The protein requirement can be represented by the inequality:
3x + y < 25
To account for the non-negativity of the servings, we also add the following constraints:
x ≥ 0
y ≥ 0
b. Now let's find three solutions that would satisfy Mark's pet's needs.
Solution 1: Let's say Mark gives his pet 3 servings of Food A and 2 servings of Food B.
For Food A:
2 servings of Food A = 2 * 3 = 6 grams of fiber
2 servings of Food A = 2 * 3 = 6 grams of protein
For Food B:
2 servings of Food B = 2 * 4 = 8 grams of fiber
2 servings of Food B = 2 * 1 = 2 grams of protein
Total fiber = 6 + 8 = 14 grams
Total protein = 6 + 2 = 8 grams
The fiber requirement (18 grams) is not satisfied, but the protein requirement is.
Solution 2: Let's say Mark gives his pet 5 servings of Food A and 1 serving of Food B.
For Food A:
5 servings of Food A = 5 * 2 = 10 grams of fiber
5 servings of Food A = 5 * 3 = 15 grams of protein
For Food B:
1 serving of Food B = 1 * 4 = 4 grams of fiber
1 serving of Food B = 1 * 1 = 1 gram of protein
Total fiber = 10 + 4 = 14 grams
Total protein = 15 + 1 = 16 grams
Neither the fiber nor the protein requirement is satisfied.
Solution 3: Let's say Mark gives his pet 4 servings of Food A and 3 servings of Food B.
For Food A:
4 servings of Food A = 4 * 2 = 8 grams of fiber
4 servings of Food A = 4 * 3 = 12 grams of protein
For Food B:
3 servings of Food B = 3 * 4 = 12 grams of fiber
3 servings of Food B = 3 * 1 = 3 grams of protein
Total fiber = 8 + 12 = 20 grams
Total protein = 12 + 3 = 15 grams
Both the fiber (20 grams) and protein (15 grams) requirements are satisfied.
These three solutions show that Solution 3 works for Mark's pet's needs.