Question 1202966
<pre>
How did you know there was only 1 solution if you didn't know how to do
the other part?  Did you just guess?

{{{(matrix(5,8,
x, y,    z, u,    v,    w, P, Constants,
0, 0, -1/2, 1, -1/4, -1/4, 0, 2,
0, 1,    0, 0,  1/4, -1/4, 0, 3,
1, 0,  3/2, 0,    0,  1/2, 0, 15,
0, 0,    1, 0,  3/2,  1/2, 1, 78))}}}

That is the matrix for this system of equations:

{{{system(expr(-1/2)z + u - expr(1/4)v - expr(1/2)w=2,
y+expr(1/4)v-expr(-1/4)w = 3,
x+expr(3/2)z+expr(1/2)w = 15,
z+expr(3/2)v+expr(1/2)w+P=78)}}}

Solve the bottom equation for P:

{{{P=78-z-expr(3/2)v-expr(1/2)w}}}

We want P to be as large as possible, and we have three non-negative numbers
subtracted from the 78.  We can keep the whole 78 for P by choosing all three
variables z, v, and w = 0.  So we substitute those in the system and get:

{{{system(u=2,
y = 3,
x = 15,
P=78)}}}

So P has a maximum value of 78 when x = 15, y = 3, and z = 0.  The point is

(x,y,z) = (15,3,0)

Edwin</pre>