Solver / limitations in changing cells

I am using Version: Build ID: 1:5.0.3~rc2-0ubuntu1~trusty2 (Kubuntu 14.04)
Please have a look at the attached sheet. It is a fictious company that needs a financing plan for the next year. The linear solver in Calc does find a solution if I just look for a solution with a short term credit. But as soon as I include the cell $B$13 in the line “by changing cells” to read “$C$12:$N$12;$B$13”, the solver complains that it is no longer a linear model.
My question: Can the linear solver in calc handle this additional cell?
Note: The solver in the competition product from Redmond can handle this. hue_lo_17nov_calc.ods