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From the definition of linear programming:

Cost function = c1x1 + c2x2 + ... + cnxn
Constraints = 
a11x1 + a12x2 + ... + a1nxn <= b1
...
am1x1 + am2x2 + ... + amnxn <= bm

What do the letters a, b and c stand for? I assume c stands for cost and a stands for assignment, but I can't figure out what b would stand for.

user2108462
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    They are just letters - they have no implicit meaning. When you choose letters that hav specific meanings in the world, you can blind yourself to the fact that the technique can be used in a lot of different ways. – Thomas Andrews Jun 21 '15 at 11:17
  • When talking about quadratic equations, for exampl, why write $ax^2+bx+c=0,$ and not some other variables? – Thomas Andrews Jun 21 '15 at 11:20
  • In the quadratic equation, a stands for the coefficient of x^2, b stands for the coefficient of x, and c stands for constant. <- This is the kind of answer I would like.. – user2108462 Jun 21 '15 at 11:23
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    It depends on the context. $c_i$ can be the unit cost of input factor $i$. And $a_{ij}$ is a coefficent. The meaning would be: It is the required amounts of ressource $j$ to produce ONE unit of $x_i$. $b_i$ is the available amount of ressource $j$. – callculus42 Jun 21 '15 at 11:27
  • That sounds good, you could post that as an answer to the question. – user2108462 Jun 21 '15 at 11:34
  • First of all, write this as $Ax\le b$, $cx\stackrel!=\max$ to make it legibly small. Then note that the "givens" are just the first three letters of the alphabet and the usage of $x$ for the unknown is also common. – Hagen von Eitzen Jun 21 '15 at 12:15
  • I don't know about linear programming, but in TV programming, they stand for Australian Broadcasting Corporation, http://www.abc.net.au – Gerry Myerson Jun 21 '15 at 12:48

1 Answers1

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It depends on the context. $c_i$ can be the unit cost (price) of input factor i . And $a_{ij}$ is a coefficent. The meaning would be: It is the amount of input factor i, which is required to produce one unit of product j$.

$b_j$ is the required amount of product j.

$x_i$ is the amount of input factor i$

Example:

You want to produce at least 10 units of product 1 and 15 units of product 2. You need 2 units of input factor 1 to produce one unit of product 1 and 2 units of input factor 1 to produce one unit of product 2. You need 3 units of input factor 1 to produce one unit of product 1 and 1 unit of input factor 1 to produce one unit of product 2.

The constraints are:

$2x_1+3x_2\geq 10$ (product 1)

$2x_1+x_2\geq 15$ (product 2)

The signs have to be $\geq$. You want at least $b_j$ amounts of product j. Otherwise the solution would be trivial.

Each unit of factor 1 costs $\$10$ and $\$12$ factor 2.

Thus the objective function is

$\texttt{min} \ \ 10x_1+12x_2$

In this case $x_1,x_2 \in \mathbb N_0$.

callculus42
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