Well water mixtures and Arsenic Levels (please help!)

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ryman88

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I need to draw water from 3 wells to meet a daily demand of 3.57 million liters and maintain an arsenic level of 8(ppb) parts per billion.

Well 1 can supply 1.5 million L per day and has an arsenic concentration of 5 ppb.

Well 2 can supply 2 million L per day and has an arsenic concentration of 12 ppb.

Well 3 can supply 1 million L per day and has an arsenic concentration of 17 ppb.

How much water must be pumped from each well to meet the 3.57 million liter daily demand, while maintaining an 8ppb arsenic level?

I have tried creating a matrix but the equations i tried to create are very far off, or do not give the answer i need. I have tried converting to percentages but then got lost and didn't know how that would make any progress. Please help!
 
What equations did you create?

1.5 + 2 + 1 = 4.5 - Check - It appears we have enough.

W = Amount of water from Well #1
X = Amount of water from Well #2
Y = Amount of water from Well #3

W <= 1.5
X <= 2.0
Y <= 1.0
W + X + Y = 3.57
What else?
 
getting the parts per billion was what i was stuck on. I tried to say make an equation to plug into a matrix but I know its wrong.

I believe that well one's arsenic concentration looks like .000,000,005 which i also thought would be .005% of the amount arsenic in the water.
Well 2 would be .012% and well 3 would be .017%

W1= water output of well 1
W2= water output of well 2
w3= water output of well 3

W1+W2+W3=3.57mil L
1.5x+2y+1z=3.57mil L

A1= arsenic level of well 1
A2= arsenic level of well 2
A3= arsenic level of well3

A1+A2+A3=8ppb
.005x+.012y+.017z=8ppb

my matrix looked like this
[1 1 1 3.57 ]
[.005 .012 .017 .008]

I think it needs a third row to give all three variables
 
?? Very odd. So many variables. You have defined "W"-variables. What are x, y, and z? Be careful and consistent.

I suppose you can try to worry about the concentration level. It might be easier to worry about the total arsenic conent.

W = Amount of water from Well #1
X = Amount of water from Well #2
Y = Amount of water from Well #3

W <= 1.5
X <= 2.0
Y <= 1.0
W + X + Y = 3.57

W(5) + X(12) + Y(17) = 3.57(8)

Substantially simpler definition, don't you think? Also, we won't mind if we get LESS arsenic, so it should be:

W(5) + X(12) + Y(17) <= 3.57(8)

Also, we can't put water back, so the other constraints should be:

0 <= W <= 1.5
0 <= X <= 2.0
0 <= Y <= 1.0

You can think and ponder for a while, but eventually, you will have to decide that you need ALL of Well #1 to ahve any chance fo making the arsenic concentration sufficiently low. Rewriting a little:

W + X + Y = 3.57
W(5) + X(12) + Y(17) <= 3.57(8)

X + Y = 3.57 - W = 3.57 - 1.50 = 2.07
X(12) + Y(17) <= 3.57(8) - 5W = 21.06

Now you've only two variables and you can proceed with your solution. However...
 
yes! a much simpler way to label and explain.

I'm confused though what does the 21.06 stand for what did we figure out I followed the math but am uncertain of the meaning.

Thank you for looking through this with me I really appreciate it.
 
It's just arithmetic. Follow the calculation carefully. You haven't yet gotten to the "however"?

When I moved W to teh other side, I assumed we used ALL of Well #1. This was not an arbitrary choice.
 
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