setting up constrained maximization


I am trying to enter the maximization problem with constraints below:

$ $ \begin{aligned} & \underset{x_0, x_1}{\text{max}} & & \Big[a(C-x)+(1-a)(z-y)\Big] \ & \text{s.t.} & & a u(x_1)+(1-a)u(y)-h \geq 0 \ & & & (a-b)(u(x)-u(y)) \geq 0 \end{aligned} $ $

as:

Maximize[{a(C-x)+(1-a)(z-y), au(x)+(1-a)u(y)-h >= 0, (a-b)(u(x)-u(z))>=0}, {x,y}] 

Is this the correct way to enter the problem- especially the u(x) and u(y) terms?