Time for some Lagrange multipliers!
Optimization function: VP(x,y)=x*y+3*x
Constraint: z(x,y)=x+y=constant
dz/dy=dz/dx=1
dVP/dy=x,dVP/dx=3+y
These vectors must be in the same direction, with a Lagrange multiplier -L applied:
(dz/dx,dz/dy)=L(dVP/dx,dVP/dy)=(L dVP/dx,L dVP/dy)
L dVP/dx=dz/dx, L dVP/dy=dz/dy
1=Lx, L=1/x
1=(3+y)/x, x=3+y