A farmer has 200 acres of land suitable for cultivating crops A, B and C. The cost per acre of cultivating crop A, crop B and crop C is $40, $60 and $80, respectively. The farmer has $12,600 available for land cultivation. Each acre of crop A requires 20 labor-hours, each acre of crop B requires 25 labor-hours and each acre of crop C requires 40 labor-hours. The farmer has a maximum of 5960 labor-hours available. If he wishes to use all his cultivatable land, the entire budget and all the labor available, how many acres of each crop should he plant? [Use the Gauss Jordan Elimination method to solve]

The labor is given as

20A+25B+40C=5960

The total land available is

A+B+C=200

The cost is:

40A+60B+80C=12600

So, the matrix is:

\begin{bmatrix}20&25&40&5960\\1&1&1&200\\40&60&80&12600\end{bmatrix}

Now, use Gaussian eleimination to solve the matrix.