How did you know there was infinitely many solutions?  I don't know how to tell
until I do the other part.

x       y       u        v      w       P	Constants
0	0	1	−23/5   12/5    0	48
0	1	0	3/5    −2/5     0	6
1	0	0	−2/5    3/5     0	21
0	0	0	0	5	1	375



That is the matrix for this system of equations:



Solve the bottom equation for P:



We want P to be as large as possible, and we have one non-negative number
subtracted from the 375.  We can keep the whole 375 for P by choosing the
variable v = 0.  So we substitute v = 0 in the system and get:



So P has a maximum value of 375. 



So since x and y depend on v and since there are infinitely many values
we can choose for v, there are infinitely many solutions.



If we choose v=0, we get the point (x,y) = (21,6) on the line, which you have.
To get another point on the line, to make it a whole number, choose a multiple
of 5, say 5, and get (x,y) = (23,3).

If you wanted a third point, choose another multiple of 5, say 10, and get
(x,y) = (25,0). 

Edwin