Question

Help please. Select all correct answers

Answer 1

We're given pairs (A,B) and asked if we have

enough calcium,

5A + 4B >= 24

enough iron

4A + 6B >= 15

and enough vitamins

7A + 4B >= 15

We check each constraint on each pair; if we find any false we can stop for that pair.

(A,B)=(1,4)

5(1)+4(4)=21 under 24, NO CHECK

(A,B)=(1,5)

5(1) + 4(5) = 25, bigger than 24, good

4(1) + 6(5) = 34, bigger than 15, good

7(1) + 4(5) = 27, bigger than 15, good CHECK

(A,B)=(2,3)

5(2)+4(3)=22, NO CHECK

(A,B)=(3,2)

5(3)+4(2)=23, NO CHECK

(A,B)=(4,1)

5(4) + 4(1) = 24, ok

4(4) + 6(1) = 22, ok

7(4) + 4(1) = 32, ok, CHECK

Answer 2

(1,5), (4,1)

Explanation:

Let's check the possible answers and see if they will Steve to meet his requirements:

We'll start by looking if each answer (dose) will provide enough calcium first. If it does, we'll get iron and vitamins if needed.

a) (1,4)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (4)

24 ≤ 5 + 16

24 ≤ 21

NO!

b) (1,5)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (5)

24 ≤ 25 YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(1) + 6(5)

15 ≤ 34 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (1) + 4 (5)

16 ≤ 27 YES

YES, YES, YES...

c) (2,3)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (2) + 4 (3)

24 ≤ 22 NO!

d) (3,2)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (3) + 4 (2)

24 ≤ 23 NO!

e) (4,1)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (4) + 4 (1)

24 ≤ 24 YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(4) + 6(1)

15 ≤ 22 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (4) + 4 (1)

16 ≤ 32 YES

YES, YES, YES...