Problem 1

Plot3D[{0,6x y^2},{x,0,1},{y,0,1},AxesLabel->Automatic,ColorFunction->"TemperatureMap",BoxRatios->{1,1,1},PlotRange->All]

Problem 2

Plot3D[{0,3x+3y},{x,0,1},{y,0,1-x},AxesLabel->Automatic,ColorFunction->"TemperatureMap",BoxRatios->{1,1,1}]