The problem consists of an objective function of two variables which is supposed to be minimized. There are two inequality constraints containing both the variables. The problem is to be solved using regional monotonicity.
The most simple way that has worked well for me is to just take the partial derivatives and see if they are positive or negative. If so, they are monotonic over the whole space. If not, they are regionally monotonic or not monotonic at all (i.e. periodic or constant functions) - you can then find the monotonicity of the regions by plotting the functions or finding roots and doing a partial-derivative second derivative test. This might involve calculating gradients/Hessians since the function is multi-variable, depending on what you choose to do.
There are several good formal definitions, like this one shown on StackExchange
https://math.stackexchange.com/questions/1198373/monotonicity-of-function-of-two-variables
and this lecture from Real Analysis at University of Chicago
http://math.uchicago.edu/~drewmoore/Math132/Lecture6.pdf
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