Question

Steve's doctor has advised him to take protein supplements. He bought two brands, Brand A and Brand B. The table gives the amount of calcium, iron, and vitamins (in milligrams per spoonful) in each of the two brands.

Brand Calcium Iron Vitamins
A 5 4 7
B 4 6 4

Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins. Which ordered pairs of values are solutions for the given system inequalities? Select all the correct answers.

A) (1, 4)
B) (1, 5)
C) (2, 3)
D) (3, 2)
E) (4, 1)

Answer 1

(1,5) and(4,1).

Explanation:

Given :

Brand Calcium Iron Vitamins

A 5 4 7

B 4 6 4

Let x be the quantity of brand A

Let y be the quantity of brand B

Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins.

So, equation becomes:

`5x+4y\geq 24`

`4x+6y\geq 15`

`7x+4y\geq 16`

Now plot the given inequalities on the graph

Refer the attached graph

Thus the points lies in the feasible region are (1,5) and(4,1).

Answer 2

Let the number of Brand A taken be x and the number of Brand B taken be y.
Then
5x + 4y ≥ 24
4x + 6y ≥ 15
7x + 4y ≥ 16

Points (1, 5) and (4, 1) satisfy the system of the given system of inequalities.