Question

Select all the correct answers. 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, where x represents the number of spoonfuls of brand A that Steve takes and y represents the number of spoonfuls of brand B that Steve takes? Select all the correct answers. (1, 4) (1, 5) (2, 3) (3, 2) (4, 1)

Answer 1

The correct options are 2 and 5.

Explanation:

The given table is

Brand A B

Calcium 5 4

Iron 4 6

Vitamins 7 4

Let, x represents the number of spoonfuls of brand A that Steve takes and y represents the number of spoonfuls of brand B that Steve takes.

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

`5x+4y\geq 24`

`4x+6y\geq 15`

`7x+4y\geq 16`

The points are (1, 4),(1, 5), (2, 3), (3, 2), (4, 1).

Check the above inequalities by each point.

All the above inequality satisfy by points (1,5) and (4,1), because (1,5) and (4,1) lie in the feasible region.

Check the inequalities for (1,5).

`5(1)+4(5)\geq 24\Rightarrow 25\geq 24`

`4(1)+6(5)\geq 15\Rightarrow 34\geq 15`

`7(1)+4(5)\geq 16\Rightarrow 27\geq 16`

All the statements are true.

Check the inequalities for (4,1).

`5(4)+4(1)\geq 24\Rightarrow 24\geq 24`

`4(4)+6(1)\geq 15\Rightarrow 22\geq 15`

`7(4)+4(1)\geq 16\Rightarrow 32\geq 16`

All the statements are true.

Therefore the correct options are 2 and 5.

Answer 2

The three inequalities are ...

`5a+4b\geq 24\\4a+6b\geq 15\\7a+4b\geq 16`

A graph is useful for this. Satisfying the constraint on calcium will satisfy the other constraints. Correct choices include (1, 5), (4, 1).