Hello pakmanThis would appear to be a fairly straightforward exercise in Linear Programming. Using the numbering above:

(3) becomes X1 - X2 >= -2 which is redundant since (4) is a stronger condition.

(6) and (4) imply X1 >= 2 which renders (5) redundant also.

So we are left with (2), (4) and (6). Plotting these on a graph, and considering the gradient of the line 2X1 + 5X2 = k, gives the maximum value 48 at (9,6).

I don't understand the need for binary.

Grandad