An initial comparison of the Gnumeric and Excel solvers indicates (that on the test problem at least) that the Gnumeic solver finds a better minimum for the optimisation problem. There are constraints in the problem but they are not active at the optimum.
The solver control panel is slightly more fussy about what it accepts than that of Excel.
The only negative observation is that at one point (when I was still constructing the sheet) a solution violated a constraint (assuming that I had implemented what I think I had). This will need watching to see if it is a real problem or just my error.