Math help!

[tonyg]

So I have these problems to do for my class, and I completed all of them just fine, except this one. I just can't quite grasp how to transform the problem into an equation, even though I was able to do so for all my other problems. If anybody could help me comprehend how to do this, it would be greatly appreciated. (I also have no idea if this is the good section or not, so mods feel free to move at your will)

There are 4 countries to which a company can send a marketing rep. The company has 14 potential workers each working in 6 separate divisions in the US. All of the meetings are on the same day, so a rep can only be at one location. Each of the 4 countries have a set demand for reps (12 total) and they must be filled completely.

Costs England India China Japan Availability
Division 1 6 500 $ 6 800 $ 6 300 $ 5 700 $ 1
Division 2 6 700 $ 7 000 $ 6 500 $ 5 400 $ 2
Division 3 6 800 $ 7 200 $ 6 900 $ 5 500 $ 3
Division 4 6 800 $ 7 500 $ 7 000 $ 5 900 $ 3
Division 5 7 100 $ 6 900 $ 7 500 $ 5 700 $ 2
Division 6 6 900 $ 7 100 $ 6 600 $ 5 900 $ 3
Demand 2 3 4 3

Basically, the objective is to minimize the costs while filling all the demand spots.

I have no fucking clue how to put this into a formula notably because

1. I can't find any relation between the costs
2. Only 12 of the 14 available reps will be used
3. Prices can be reused again, as in, if I choose to send the 2 guys available from Division 2 to Japan, it'll cost me 5400x2, but I could also choose to send one to Japan and one to India.

Any help would be greatly appreciated

[Mojo]

Your table looks like shit.

Costs 	    England  India   China   Japan   Availability
Division 1  $6,500   $6,800  $6,300  $5,700  1
Division 2  $6,700   $7,000  $6,500  $5,400  2
Division 3  $6,800   $7,200  $6,900  $5,500  3
Division 4  $6,800   $7,500  $7,000  $5,900  3
Division 5  $7,100   $6,900  $7,500  $5,700  2
Division 6  $6,900   $7,100  $6,600  $5,900  3
Demand 	    2	     3	     4	     3

Here's a better one.

[Byrthnoth]

I'm honestly not sure how to do this either. It's probably some kind of matrix manipulation question and I'd be interested in seeing the real way to solve it, but my guess is:
China - Division 1, Division 2, Division 2, Division 6 - 25900
India - Division 5, Division 5, Division 6 - 20900
England - Division 4, Division 4 - 13600
Japan - Division 3, Division 3, Division 3 - 16500
Total: $76,900


I got this by averaging each column and making a table of the residuals (the difference between the given values and the averages). Then I assigned people in the order of increasing residual, so I assigned the most negative number first, next most negative number second, etc, marking when I'd used up a row worth of people.

[Mojo]

Some cursory thoughts~

You can probably approach this by setting up a system of equations.

E = e1*6500+e2*6700+e3*6800+e4*6800+e5*7100+e6*6900
I = i1*6800+i2*7000+i3*7200+i4*6500+i5*6900+i6*6600
C = c1*6300+c2*6500+c3*6900+c4*7000+c5*7500+c6*6600
J = j1*5700+j2*5400+j3*5500+j4*5900+j5*5700+j6*5900

T = E+I+C+J

e1+e2+e3+e4+e5=2
i1+i2+i3+i4+i5=3
c1+c2+c3+c4+c5=4
j1+j2+j3+j4+j5=3

That's a start. I don't really have the time to continue right now.

[tonyg]

It was just what I needed to see it logically in my head, I solved it an hour later using Excel's solver. Much thanks to you sir <3