Question

**MEDAL + FAN**

A city wants to plant maple and spruce trees to absord carbon dioxide. It has $2100 to spend on planting spruce and maple trees. The city has 45,000ft^2 avaible for planting.

Write the constraints for the situation.

SPRUCE MAPLE
Planting Cost | $30 | $40
Area Required | 600 ft^2 | 900 ft^2
Carbom Dioxide | 650 lb/yr| 300 lb/yr
Absorption

Answer 1

@wio
@pitamar
Amyways ideas? I'm very confused :/

Answer 2

Any* ideas

Answer 3

Eh, before I post anything... Could you help me with terms? English is not my native language, and I'm not confident enough posting blindly...
What absorption means?

Answer 4

No prob. Absorption means the process or action by which one thing absorbs or is absorbed by another.

Answer 5

Soaking up, basically. Haha

Answer 6

And just to make sure... you want to find how would it be with 'field of maples' and 'field of spruces'?

Answer 7

Well, Using the data from the table, I want to be able to write the constraints for the situation.

Answer 8

Well, by data, spruce costs less, produces more and requires less space. So if we want more production we would prefer spruces.
If we would be planting spruce trees then we know that we have 45,000ft^2 to plant. that means:
\[
\frac{\text{Available space}}{\text{Required for tree}} = \frac{45,000_{ft^2}}{600_{ft^2}} = 75 \text{ trees}
\]
But $2100 / $30 = 70, so we can afford only 70 spruce trees:
\[
\small (\text{Number of trees}) \cdot (CO_2\text{ production}) \normalsize = 70 \cdot 650_{lb/year} = 45,500_{lb/year}
\]
If i'm getting it right, maple is worse in every factor, so we wouldn't like to plant any of it.

Answer 9

Man, I feel dumb..

Answer 10

I have a feeling I'm still being confused. terribly sorry.. I'll be reading again.. and again... I'm missing something, that's for sure =[

Answer 11

You're doing good! :) It looks great!

Answer 12

Im not sure if you missed anything because I'm rather confused myself...haha

Answer 13

Doesn't feel like that. but sure, thanks

Answer 14

Your work does look very good though.

Answer 15

ok, anything else?

Answer 16

Well, for the name question, it says "Write the objective function."

Answer 17

Well, if we're trying to get the opposite effect of this.. Like, trying to get minimal absorption and yet using all the money... then... Let's go with maple
\[
\frac{\text{Available space}}{\text{Required for tree}} = \frac{45,000_{ft^2}}{900_{ft^2}} = 50 \text{ trees}
\]
$2100 / $40 = 52.5
But we can only plant 50 maple trees anyway in that space.. so
\[
50 \cdot 300_{lb/year} = 15,000_{lb/year}
\]
And since we have no space left... that's all we planted.
So 15000 seems to be the minimum we can get in those conditions

Answer 18

Well done! :D
Is that the whole function?

Answer 19

Sorry, I seem to misunderstood the term once again.. damnit.. reading reading..

Answer 20

No no, you're fine!

Answer 21

Ok after abit reading it seems like this.
Let:
\[
x_1 = \text{Spruces} \\
x_2 = \text{Maples}
\]
Then.. Function:
\[
\max f(x) = 650 \cdot x_1 + 300 \cdot x_2
\]
constraints:
\[
30 \cdot x_1 + 40 \cdot x_2 \le 2,100 \\
600 \cdot x_1 + 900 \cdot x_2 \le 45,000
\]
After abit reading here:
http://en.wikipedia.org/wiki/Constraint_(mathematics)
To understand what the heck is this all about...

Answer 22

And by this..
http://www.businessdictionary.com/definition/objective-function.html
Does that look more like it should now?

Answer 23

Oh i see now! I see the function..

Answer 24

Do you mind helping me with a bit more?

Answer 25

Sure... not that i know any of it.. never learned math =|
But why not

Answer 26

You're helping me greatly. Haha.
Anyways, the next one is "Graph the feasible region and find the vertices." (still using the original spruce and maple tree data)

Answer 27

Ok, got in here:
http://en.wikipedia.org/wiki/Feasible_region
Look at the graph there, you see how the 3 blue lines limit the possible solutions?

Answer 28

Yes, I see it.

Answer 29

That 'region' trapped in between all of those is what you're looking for.
In our case we don't have 'x' and 'y'.. we have two other axis x1 and x2.
Do you want to try by yourself? or just want me to send a picture

Answer 30

Well, the problem is that I'm not sure how to exactly do it :( could you please send a pic? If it's inconvient though, it;ll be fine.

Answer 31

Well, do you know to graph a straight line function?

Answer 32

Kinda.

Answer 33

Well... I guess best way is to show you, I could host a presentation with teamviewer if you wish, show you what I mean.. I can't really do it here... too... inconvenient

Answer 34

I don't know what a teamview is, but sure :D

Answer 35

It is a program for screen sharing, you download it and enter ID and password and you can see somebody's else's computer
www.teamviewer.com

Answer 36

Do you have a skype? We can also do the same thing there.

Answer 37

pitamar2

Answer 38

I forgot that pass for pitamar... heh..

Answer 39

lol alright i'll hop on now

Answer 40

You're from Israel, right?

Answer 41

yes