I have an Alienware m11x with Optimus Technology. I setup (Fresh Install) Ubuntu 12.04 with bumblebee as below. Please help me set up the HDMI output so that I can connect it to my monitor.

$ uname -a
Linux ubuntu 3.2.0-24-generic-pae #39-Ubuntu SMP Mon May 21 18:54:21 UTC 2012 i686 i686 i386 GNU/Linux

$ lspci | grep -i vga
00:02.0 VGA compatible controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09)
01:00.0 VGA compatible controller: NVIDIA Corporation GF108 [GeForce GT 540M] (rev a1)

$ dpkg --get-selections
bumblebee                                       install
bumblebee-nvidia                                install

$ bumblebeed -version
bumblebeed --version
bumblebeed (Bumblebee) 3.0
Copyright (C) 2011 The Bumblebee Project

Should xrandr normally show HDMI?

$ xrandr -q     
Screen 0: minimum 320 x 200, current 1366 x 768, maximum 8192 x 8192
LVDS1 connected 1366x768+0+0 (normal left inverted right x axis y axis) 256mm x 144mm
   1366x768       60.0*+
   1360x768       59.8     60.0  
   1024x768       60.0  
   800x600        60.3     56.2  
   640x480        59.9  
VGA1 disconnected (normal left inverted right x axis y axis)



$ cat /etc/X11/xorg.conf 
Section "ServerLayout"
    Identifier "Layout0"
EndSection

Section "Device"
    Identifier "Device1"
    Driver "nvidia"
    VendorName "NVIDIA Corporation"
    Option "NoLogo" "true"
    Option "ConnectedMonitor" "DFP"
EndSection

$ cat /etc/bumblebee/xorg.conf.nvidia 
Section "ServerLayout"
    Identifier "Layout0"
EndSection

Section "Device"
    Identifier "Device1"
    Driver "nvidia"
    VendorName "NVIDIA Corporation"
    Option "NoLogo" "true"
    Option "ConnectedMonitor" "DFP"
EndSection

$ cat /etc/bumblebee/xorg.conf.nouveau 
Section "ServerLayout"
    Identifier     "Layout0"
    Screen         "Screen0"
    Option         "AutoAddDevices" "true"
EndSection

Section "Device"
    Identifier     "Device0"
    Driver         "nouveau"
EndSection

Section "Screen"
    Identifier     "Screen0"
    Device         "Device0"
EndSection

and finally the biggest config file below:

$cat /etc/bumblebee/bumblebee.conf 
[bumblebeed]
VirtualDisplay=:8
KeepUnusedXServer=true
ServerGroup=bumblebee
TurnCardOffAtExit=false
NoEcoModeOverride=false
Driver=

[optirun]
VGLTransport=proxy
AllowFallbackToIGC=false
PMMethod=none

[driver-nvidia]
KernelDriver=nvidia-current
Module=nvidia
PMMethod=none
LibraryPath=/usr/lib/nvidia-current:/usr/lib32/nvidia-current
XorgModulePath=/usr/lib/nvidia-current/xorg,/usr/lib/xorg/modules
XorgConfFile=/etc/bumblebee/xorg.conf.nvidia

[driver-nouveau]
KernelDriver=nouveau
PMMethod=none
XorgConfFile=/etc/bumblebee/xorg.conf.nouveau

Any ideas on setting up the Optimus to output to the HDMI T.V.?

I want to enable my HDMI with my GeForce GT 540M.