## anonymous one year ago 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.

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1. nincompoop

select where?

2. UsukiDoll

I think it's misaligned |dw:1436246092831:dw|

3. anonymous

yes, it is out of alignment...calcium is 5, iron is 4 and vitamins are 7 for brand A. Brand B has calcium 4, iron is 6 and vitamins are 4. the possible solutions (ordered pairs) are: (1,4) ; (1,5) ; (2,3) ; (3,2) or (4,1)

4. ganeshie8

|dw:1436246945999:dw|

5. ganeshie8

It is given that `Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins` One way to approach this problem is to graph the inequalities corresponding to the 3 inequalities and simply pick the points that belong to common region : \[5A+4B\ge 24\tag{1}\] \[4A+6B\ge 16\tag{2}\] \[7A+4B\ge 15\tag{3}\]

6. ganeshie8

graphing the inequalities gives us |dw:1436247354463:dw| simply pick the ordered pairs that belong to the common region

7. ganeshie8

below, the common region is shaded in light blue : |dw:1436247428915:dw| we just need to figure out which ordered pairs fall in this region

8. ganeshie8

For example, the ordered pair `(1,4)` is not a solution because it doesn't fall in the common region : |dw:1436247749735:dw|

9. anonymous

I'm sorry, but I don't see a light blue area on the graph??? If you are looking at the lighter colored purple region, I don't see any of the ordered pairs fitting into this area.

10. ganeshie8

Thats okay, the actual color is not important at all. Its the common region that you need to figure out from the graphs. Can you plot `(1, 5)` in above graph ?

11. anonymous

i think so

12. ganeshie8

do it

13. anonymous

ok, it looks like 1,5 falls w/in the common region of all three lines

14. ganeshie8

good, so (1,5) is indeed a solution. just so you know, you may click the "pencil" button on top right corner of a drawing to reply.. it actually pastes that drawing in your reply so that you may annotate over it

15. ganeshie8

|dw:1436248626643:dw|

16. ganeshie8

How about remaining ordered pairs, do any of them fall in the common region ?

17. anonymous

I think 4,1 falls on the line...so would ordered pairs falling on the line be included in the solution set for non-strict inequalities?

18. ganeshie8

Absolutely! "at least" refers to non-strict inequality, so the boundary points are also part of the solution set.

19. ganeshie8

|dw:1436249074491:dw|

20. ganeshie8

|dw:1436249204439:dw|

21. anonymous

Thanks for your help! The graph really helped.

22. ganeshie8

Glad it helped, yw! Btw there is an alternative : You could plugin each of the given ordered pairs into the inequalities and pick the ordered pairs that satisfy all the inequalities. This is more algebra and doesn't give as much insight as the graphs give... But you should also get used to this alternative method as graphing might not be always possible.. good luck!