Question 1202912
<pre>
{{{(matrix(4,6,
x,y,u,v,P,k,
1,1,1,0,0,1,
1,0,-1,1,0,5,
5,0,7,0,1,18))}}}

Change to a system of equations:

{{{system(1x+1y+1u+0v+0P=1, 1x+0y-1u+1v+0P=5,5x+0y+7u+0v+1P=18)}}}

Simplify:
{{{system(x+y+u=1, x-u+v=5,5x+7u+P=18)}}}

All of the variables are non-negative.  Solve the last equation for P:

{{{P=18-5x-7u}}}

To make P large as possible choose what is subtracted from it to be 0,
so we can keep the whole 18 for P if we choose x = 0 and u = 0.
Substituting:

{{{system(0+y+0=1, 0-0+v=5,5(0)+7(0)+P=18)}}}

{{{system(y=1,v=5,P=18)}}}

Choose x = 0, y = 1, for a maximum value of P = 18.

Edwin</pre>